title: Leigh Whannell

text: Around the same time, Whannell returned to collaborate with Wan; they wrote a film called "Dead Silence", which Wan directed. It was originally slated for a 2006 release, but small problems with the title pushed the release date back to March 2007. In 2006, the duo composed the story for "Saw III"; Whannell wrote the screenplay for the third time. It was again directed by Bousman and was released on 27 October 2006. Whannell has a featured cameo, reprising his role as Adam. "Saw III" grossed $33,610,391 on its opening weekend, making around $129,927,001 worldwide (after 38 days in cinemas) and is currently the most successful "Saw" film to date.


title: Leigh Whannell

text: Whannell's writing partner, Wan, was chosen to direct the film "Death Sentence", the first feature film with their participation that they did not write themselves. Whannell has a small role as Spink in "Death Sentence".


title: Leigh Whannell

text: In 2008, Whannell took off his "writing hat" to perform alongside Nathan Phillips in "Dying Breed", a low-budget Australian horror film about a team of zoologists exploring the Tasmanian wilderness to locate a creature thought extinct, the thylacine, or Tasmanian tiger. Instead, they wander into the domain of cannibals who retain their ancestor Alexander Pearce's taste for human flesh, and become prey.


title: Leigh Whannell

text: Before and during the production of "Saw", Whannell sought medical treatment. "I was going through a bit of a tough time healthwise and suffering anxiety," says Whannell. "The anxiety manifested itself in physical ways. I was suffering headaches everyday for nearly a year. It was serious stuff and really started affecting my life." Spending time in a hospital inspired him to endow the lead antagonist of the "Saw" series, John Kramer / Jigsaw, with cancer. "It was weird to be 25 and sitting in a neurological ward and I'm surrounded by people who actually had brain tumors. It was very scary and it was my first proper look at mortality. I really wanted to get my health back and it really hammered home how important good health is. If you've got that, you've got everything".


title: Leigh Whannell

text: Whannell wrote the script for and acted in the 2011 paranormal thriller film, "Insidious", which was directed by Wan and produced by Oren Peli.


title: Leigh Whannell

text: It's hard to say definitively, because we don't own the copyright for it. The producers could make 10 more if they wanted to. But, if we're to take them at face value, they told us that they were definitely done with it. They're pretty exhausted. They've been making one a year every year for the past seven years, so I think they need some time off.


title: Leigh Whannell

text: Media reports were published in mid-2013 in regard to "Cooties", a film project that Whannell is an executive producer, actor and screenwriter for. The film's plot concerns an extreme virus that infects an isolated elementary school. Whannell made his directing debut on the sequel "" (2015), which he also wrote.


title: Leigh Whannell

text: In 2014, Whannell expressed possible interest in returning to the "Saw" franchise; however, in a November 2013 post on his personal blog, Whannell described a new chapter beyond his partnership with Wan, as the director had finally reached his goal of making epic-style blockbuster productions. Whannel explained: "Now, he's off making the films he's always wanted to make - the big ones. I have no doubt that his name will be added to that special club of film directors that he's always admired very soon. I'm so happy for him, like a proud father. And that is why it is the end of an era." Whannell also added that he doesn't rule out collaborating with Wan again, but he felt like he needs to direct a film for the first time.


title: Leigh Whannell

text: Whannell was writer-director of the science fiction body horror film "Upgrade", which was released by Blumhouse Tilt and OTL Releasing in 2018 to positive reception. Whannell next wrote, directed, and co-executive produced a retooling of H.G. Wells' book "The Invisible Man". The film starred Elisabeth Moss and Oliver Jackson-Cohen, and was released in 2020 to universal critical acclaim. In July 2020, it was announced that he's working on a sequel to "The Invisible Man". Whannell is currently working on a reboot of "Escape from New York". He's also producing and directing a sequel series to "Upgrade".


title: AGM-158 JASSM

text: The AGM-158 JASSM (Joint Air-to-Surface Standoff Missile) is a low observable standoff air-launched cruise missile developed by Lockheed Martin for the United States Armed Forces. It is a large, stealthy long-range weapon with a armor piercing warhead. It completed testing and entered service with the U.S. Air Force in 2009, and has entered foreign service in Australia, Finland, and Poland as of 2014. An extended range version of the missile, the AGM-158B JASSM-ER (Joint Air-to-Surface Standoff Missile-Extended Range), entered service in 2014. By September 2016, Lockheed Martin had delivered 2,000 total JASSMs comprising both variants to the USAF.


title: AGM-158 JASSM

text: The JASSM project began in 1995 after the cancellation of the AGM-137 TSSAM project. The TSSAM was designed as a high precision stealthy missile for use at stand-off ranges, but poor management of the project resulted in rising costs. Since the requirement for such weapons still existed, the military quickly announced a follow-up project with similar goals. Initial contracts for two competing designs were awarded to Lockheed Martin and McDonnell Douglas in 1996, and the missile designations AGM-158A and AGM-159A were allocated to the two weapons. Lockheed Martin's AGM-158A won and a contract for further development was awarded in 1998.


title: AGM-158 JASSM

text: The AGM-158A is powered by a Teledyne CAE J402 turbojet. Before launch the wings are folded to reduce size. Upon launch the wings deploy automatically. There is a single vertical tail. Guidance is via inertial navigation with global positioning system updates. An imaging infrared seeker provides target recognition and terminal homing. A data link allows the missile to transmit its location and status during flight, allowing improved bomb damage assessment. The warhead is a WDU-42/B penetrator. The JASSM may be carried by a wide range of aircraft: the F-15E; F-16; F/A-18; F-35; B-1B; B-2; and B-52 are all intended to carry the weapon.


title: AGM-158 JASSM

text: The Center for Strategic and Budgetary Assessments (CSBA) has suggested lightening the warhead of the AGM-158A to increase its range. That way it would be able to be fired a greater distance from enemy air defenses while being cheaper and available in greater numbers for protracted conflicts than the AGM-158B JASSM-ER variant.


title: AGM-158 JASSM

text: In 1999, powered flight tests of the missile began. These were successful, and production of the JASSM began in December 2001. The weapon began operational testing and evaluation in 2002. Late that year, two missiles failed tests and the project was delayed for three months before completing development in April 2003. Two more launches failed, this time as a result of launcher and engine problems. In July 2007, a $68 million program to improve JASSM reliability and recertify the missile was approved by the Pentagon. A decision on whether to continue with the program was deferred until spring 2008. Lockheed agreed to fix the missiles at its own cost and tightened up its manufacturing processes.


title: AGM-158 JASSM

text: On 27 August 2009, David Van Buren, assistant secretary of the Air Force for acquisition, said that there would be a production gap for the JASSM while further tests were held. Further tests in 2009 were more successful however, with 15 out of 16 rounds hitting the intended target, well above the 75% benchmark set for the test. This cleared JASSM for entry into service. The United States Air Force plans to acquire up to 4,900 AGM-158 missiles. Meanwhile, the United States Navy had originally planned to acquire 453 AGM-158 missiles but instead pulled out of the program in favor of retaining the proven AGM-84 SLAM-ER.


title: AGM-158 JASSM

text: In 2006 the Australian government announced the selection of the Lockheed Martin JASSM to equip the Royal Australian Air Force's F/A-18 Hornet fighters. This announcement came as part of a program to phase out the RAAFs F-111C strike aircraft, replacing the AGM-142 Popeye stand off missile and providing a long-range strike capability to the Hornets. JASSM was selected over the SLAM-ER after the European Taurus KEPD 350 withdrew its tender offer, despite the KEPD 350 being highly rated in the earlier RFP process, due to their heavily involvement in the series preparation for the German Air Force, their troop trials in South Africa and their final negotiations with the Spanish Air Force which finally led to a contract. As of mid-2010 the JASSM is in production for Australia and will soon enter service.


title: AGM-158 JASSM

text: Finland had also previously planned to purchase JASSM missiles for the Finnish Air Force as part of modernization plans of its F/A-18 Hornet fleet. However, in February 2007 the United States declined to sell the missiles, while agreeing to proceed as planned with other modernization efforts (the so-called Mid-Life Update 2, or MLU2). This episode led to speculation in the Finnish media on the state of Finnish – American diplomatic relations. However, in October 2011 the US DSCA announced that they had given permission for a possible sale to Finland. An order, valued 178.5 million Euros was placed in March 2012. and since Lockheed has received three Finnish integration-related projects. Finland's integration work was originally scheduled to be completed by the end of 2016, but didn't complete until March 2018 when Finnish F/A-18 Hornets successfully test fired two JASSM missiles at Naval Air Weapons Station (NAWS) China Lake.


title: AGM-158 JASSM

text: In 2013 South Korea sought the JASSM to boost the South Korean Air Force's striking capability but was refused by Washington.


title: AGM-158 JASSM

text: In 2014, Poland requested US Congressional approval for the purchase of the AGM-158 JASSM to extend the deep penetration strike capabilities of their F-16 Block 52+ fighters. Congress approved the sale in early October, and negotiations concluded in early November 2014. Poland signed a $250 million contract to upgrade its F-16s and equip the jets with (AGM-158) JASSM advanced cruise missiles in a ceremony at Poznan AB, Poland, on 11 December 2014. The missiles are expected to enter operational service in 2017, and Poland is contemplating an additional purchase for the long-range JASSM-ER version. In December 2015 the production contract for Lot 13 was signed. The contract includes 140 JASSMs for Finland, Poland and the US, 140 JASSM-ER missiles for the US, and data, tooling and test equipment. It is said to be the last production lot that will include non-ER versions. Poland's first modified F-16s should be ready by 2017, when the first missiles are delivered. The work is scheduled to be complete by June 29, 2019. In November 2016 The U.S. State Department approved the possible sale of 70 AGM-158B JASSM-ER to Poland.


title: AGM-158 JASSM

text: The US Air Force studied various improvements to the AGM-158, resulting in the development of the JASSM-Extended Range (JASSM-ER), which received the designation AGM-158B in 2002. Using a more efficient engine and larger fuel volume in an airframe with the same external dimensions as the JASSM, the JASSM-ER is intended to have a range of over as compared to the JASSM's range of about . Other possible improvements were studied but ultimately not pursued, including a submunition dispenser warhead, new types of homing head, and a new engine giving ranges in excess of . The JASSM-ER has 70% hardware commonality and 95% software commonality with the original AGM-158 JASSM.


title: AGM-158 JASSM

text: The first flight test of the JASSM-ER occurred on May 18, 2006 when a missile was launched from a U.S. Air Force B-1 bomber at the White Sands Missile Range in New Mexico. The initial platform for the JASSM-ER is the B-1. While both the original JASSM and the JASSM-ER are several inches too long to be carried in the internal weapons bay of the F-35 Lightning II, the F-35 will be able to carry both missiles externally, which would compromise the aircraft's stealth features.


title: AGM-158 JASSM

text: The JASSM-ER entered service with the USAF in April 2014. Although the B-1 was initially the only aircraft able to deploy it, it was later integrated onto the B-52, F-15E, and F-16; the B-1B can carry a full load of 24 JASSM-ERs, the B-2 16 missiles, and the B-52 outfitted with the 1760 Internal Weapons Bay Upgrade (IWBU) is able to carry 20 JASSM-ERs, eight internally and 12 on external pylons. It is also carried on U.S. Navy F/A-18E/F Super Hornet and F-35C fighters. The Air Force approved full-rate production of the JASSM-ER in December 2014. Integration of the JASSM-ER onto the B-52 and F-16 was expected to wrap up in 2018, with the F-15E completed after that; it was announced that the JASSM-ER achieved full operational capability on the F-15E in February 2018. Lot 15 production contract, awarded in June 2017 was the first consisting entirely JASSM-ER.


title: AGM-158 JASSM

text: On 14 May 2015, the head of the Air Force Research Laboratory nominated the JASSM-ER as the optimal air vehicle to carry the Counter-electronics High Power Microwave Advanced Missile Project (CHAMP) payload. CHAMP is an electronic warfare technology that fries electronic equipment with bursts of high-power microwave energy, non-kinetically destroying them. The JASSM-ER was chosen because it is an operational system, so CHAMP is to be miniaturized into the operationally relevant system.


title: AGM-158 JASSM

text: In November 2019, the Air Force retired the AGM-86C/D air-launched cruise missile (ALCM), a conventional warhead-equipped version of the nuclear-tipped ALCM, with its role replaced by the JASSM-ER.


title: AGM-158 JASSM

text: In September 2021, Australian Prime Minister Scott Morrison announced that Australia would acquire the JASSM-ER for the RAAF's F/A-18F Super Hornet and F-35A fighters.


title: AGM-158 JASSM

text: The JASSM-ER is also the basis for Long Range Anti-Ship Missile, which is a JASSM-ER with a new seeker. The Air Force used the B-1 Lancer to complete a captive carry test of an LRASM to ensure the bomber can carry it, as both missiles use the same airframe. The LRASM was not originally planned to be deployed on the B-1, being intended solely as a technology demonstrator, but in February 2014 the Pentagon authorized the LRASM to be integrated onto air platforms, including the Air Force B-1, as an operational weapon to address the needs of the Navy and Air Force to have a modern anti-ship missile. In August 2015, the Navy officially designated the air-launched LRASM as "AGM-158C". The LRASM achieved Early Operational Capability on the B-1B in December 2018.


title: AGM-158 JASSM

text: In March 2016, Lockheed Martin began analysis on an enhanced wing design to further increase range. In September 2018, the corporation was awarded a contract to develop an "Extreme Range" variant of the AGM-158. The weapon would weigh about and deliver a warhead out to a range of . Originally called the JASSM-XR and later designated the AGM-158D, it features a new missile control unit, changes to the wings, a different paint coating, an Electronic Safe and Arm Fuze, secure GPS receiver, and program protection requirements at a unit cost of $1.5 million. Low-rate initial production began in 2021 as part of Lot 19 with deliveries beginning in January 2024 at a rate of five per month for the first 40 missiles. The designation was later changed again to the AGM-158B-2.


title: AGM-158 JASSM

text: In 2020 and 2021, the Air Force Research Laboratory and Lockheed developed and tested Rapid Dragon, a multiple AGM-158 launcher module to be airdropped by C-130 or C-17 cargo planes as a low cost method of rapidly providing a surge of mass fired JASSMs using unmodified airlift assets.


title: AGM-158 JASSM

text: On 09 November 2022, Rapid Dragon was demonstrated off Norway in the Norwegian Sea at the Andøya Space Defense Range using a MC-130J Commando II from the 352nd Special Operations Wing (67th Special Operations Squadron), as part of Exercise Atreus.


title: AGM-158 JASSM

text: The JASSM was first employed during the 14 April 2018 missile strikes against Syria during the Syrian Civil War. Two B-1 Lancers fired a total of 19 JASSMs as part of strikes against three Syrian government alleged chemical weapons targets. All 19 JASSM missiles were fired at the Barzah Research Center, which was destroyed in the strike. According to Russian state media, two missiles that failed to detonate were found by the Syrian Arab Army and transferred to Russia on 18 April for study - no evidence of this claim has been provided; initial reports had stated JASSM-ER missiles were used, but it was later clarified that baseline JASSM models were employed.


title: AGM-158 JASSM

text: On 27 October 2019, at the end of the Barisha raid to capture or kill Abu Bakr al-Baghdadi, the then-leader of the Islamic State of Iraq and the Levant (ISIL) terror organization, a number of AGM-158B missiles were used to completely level the compound where the raid took place, marking the second time the missile has been used in combat.


title: Rapier

text: A rapier () or is a type of sword with a slender and sharply-pointed two-edged blade that was popular in Western Europe, both for civilian use (dueling and self-defense) and as a military side arm, throughout the 16th and 17th centuries.


title: Rapier

text: Important sources for rapier fencing include the Italian Bolognese group, with early representatives such as Antonio Manciolino and Achille Marozzo publishing in the 1530s, and reaching the peak of its popularity with writers of the early 1600s (Salvator Fabris, Ridolfo Capo Ferro).


title: Rapier

text: In Spain, rapier fencing came to be known under the term of ("dexterity") in the second half of the 16th century, based on the theories of Jerónimo Sánchez de Carranza in his work ("The Philosophy of Arms and of their Dexterity and of Aggression and the Christian Defence"), published in 1569. The best known treatise of this tradition was published in French, by Girard Thibault, in 1630.


title: Rapier

text: The French small sword or court sword of the 18th century was a direct continuation of this tradition of fencing, adapted specifically for dueling.


title: Rapier

text: The term "rapier" comes from the french term "rapière" and appears both in English and German, near-simultaneously, in the mid-16th century, for a light, long, pointed two-edged sword. It is a loan from Middle French "espee rapiere", first recorded in 1474, a nickname meaning "grater". The origin of the rapier shape is more than likely Spanish. Its name is a "derisive" description of the Spanish term "ropera". The Spanish term refers to a sword used with clothes ("espada ropera", dress sword), due to it being used as an accessory for clothing, usually for fashion and as a self-defense weapon. The 16th-century German "rappier" described what was considered a "foreign" weapon, imported from Italy, Spain or France. Du Cange in his Middle Latin dictionary cites a form "Rapperia" from a Latin text of 1511. He envisages a derivation from Greek ραπίζειν "to strike." Adelung in his 1798 dictionary records a double meaning for the German verb "rappieren": "to fence with rapiers" on one hand, and "to rasp, grate (specifically of tobacco leaves)" on the other.


title: Rapier

text: The terms used by the Italian, Spanish and French masters during the heyday of this weapon were simply the equivalent of "sword", i.e. "spada", "espada", and "épée" ("espée"). When it was necessary to specify the type of sword, Spanish used "espada ropera" ("dress sword", recorded 1468), and Italian used "spada da lato" "side-sword" or "spada da lato a striscia" (in modern Italian simply "striscia" "strip"), sometimes also called "Stocco".The Spanish name was registered for the first time in las Coplas de la panadera, by Juan de Mena, written between 1445 and 1450 approximately.


title: Rapier

text: Clements (1997) categorizes thrusting swords with poor cutting abilities as rapiers, and swords with both good thrusting and cutting abilities as cut and thrust swords.


title: Rapier

text: The word "rapier" generally refers to a relatively long-bladed sword characterized by a protective hilt which is constructed to provide protection for the hand wielding the sword. Some historical rapier samples also feature a broad blade mounted on a typical rapier hilt. The term "rapier" can be confusing because this hybrid weapon can be categorized as a type of broadsword. While the rapier blade might be broad enough to cut to some degree (but nowhere near that of the wider swords in use around the Middle Ages such as the longsword), it is designed to perform quick and nimble thrusting attacks. The blade might be sharpened along its entire length or sharpened only from the center to the tip (as described by Capoferro). Pallavicini, a rapier master in 1670, strongly advocated using a weapon with two cutting edges. A typical example would weigh and have a relatively long and slender blade of or less in width, or more in length and ending in a sharply pointed tip. The blade length of quite a few historical examples, particularly the Italian rapiers in the early 17th century, is well over and can even reach .


title: Rapier

text: The term "rapier" generally refers to a thrusting sword with a blade longer and thinner than that of the so-called side-sword but much heavier than the small sword, a lighter weapon that would follow in the 18th century and later, but the exact form of the blade and hilt often depends on who is writing and when. It can refer to earlier "Spada da lato" and the similar "espada ropera", through the high rapier period of the 17th century through the small sword and duelling swords; thus context is important in understanding what is meant by the word. (The term side-sword, used among some modern historical martial arts reconstructionists, is a translation from the Italian "spada da lato"—a term coined long after the fact by Italian museum curators—and does not refer to the slender, long rapier, but only to the early 16th-century Italian sword with a broader and shorter blade that is considered both its ancestor and contemporary.)


title: Rapier

text: Rapiers often have complex, sweeping hilts designed to protect the hand wielding the sword. Rings extend forward from the crosspiece. In some later samples, rings are covered with metal plates, eventually evolving into the cup hilts of many later rapiers. There were hardly any samples that featured plates covering the rings prior to the 1600s. Many hilts include a knuckle bow extending down from the crosspiece protecting the grip, which was usually wood wrapped with cord, leather or wire. A large pommel (often decorated) secures the hilt to the weapon and provides some weight to balance the long blade.


title: Rapier

text: Various rapier masters divided the blade into two, three, four, five or even nine parts. The forte, strong, is that part of the blade closest to the hilt; in cases where a master divides the blade into an even number of parts, this is the first half of the blade. The debole, weak, is the part of the blade which includes the point and is the second half of the blade when the sword is divided into an even number of parts. However, some rapier masters divided the blade into three parts (or even a multiple of three), in which case the central third of the blade, between the forte and the debole, was often called the medio, mezzo or the terzo. Others used four divisions (Fabris) or even 12 (Thibault).


title: Rapier

text: The ricasso is the rear portion of the blade, usually unsharpened. It extends forward from the crosspiece or quillion and then gradually integrates into the thinner and sharper portion of the blade.


title: Rapier

text: There was historical disagreement over how long the ideal rapier should be, with some masters, such as Thibault, denigrating those who recommended longer blades; Thibault's own recommended length was such that the cross of the sword be level with the navel (belly button) when standing naturally with the point resting on the ground. A small number of rapiers with extending blades were made with 4 surviving in modern collections. The purpose of the ability is unclear, with suggestions including trying to gain the advantage of surprise in a duel or an attempt to get around laws limiting weapon length.


title: Rapier

text: Rapiers are single-handed weapons and they were often employed with off-hand bucklers, daggers, cloaks and even second swords to assist with defense. A buckler is a small round shield that was used with other blades as well, such as the arming-sword. In Capo Ferro's "Gran Simulacro", the treatise depicts how to use the weapon with the rotella, which is a significantly bigger shield compared with the buckler. Nevertheless, using rapier with its parrying dagger is the most common practice, and it has been arguably considered as the most suited and effective accompanying weapon for the rapier. Even though the slender blade of rapier enables the user to launch quick attack at a fairly long and advantaged distance between the user and the opponent and the protective hilt can deflect the opponent's blade when he or she uses rapier as well, the thrust-oriented weapon is weakened by its bated cutting power and relatively low maneuverability at a closer distance, where the opponent has safely passed the reach of the rapier's deadly point. Because of such insufficient cutting power and maneuverability at this situation when the opponent passes the deadly point, this scenario leaves opening for the opponent to attack the user. Therefore, some close-range protection for the user needs to be ensured if the user intends to use the rapier in an optimal way, especially when the opponent uses some slash-oriented sword like a sabre or a broadsword. A parrying dagger not only enables the users to defend in this scenario in which the rapier is not very good at protecting the user, but also enables them to attack in such close distance.


title: Rapier

text: The "espada ropera" of the 16th century was a cut-and-thrust civilian weapon for self-defense and the duel, while earlier weapons were equally at home on the battlefield. Throughout the 16th century, a variety of new, single-handed civilian weapons were being developed. In 1570 the Italian master Rocco Bonetti first settled in England advocating the use of the rapier for thrusting as opposed to cutting or slashing when engaged in a duel. Nevertheless, the English word "rapier" generally refers to a primarily thrusting weapon, developed by the year 1600 as a result of the geometrical theories of such masters as Camillo Agrippa, Ridolfo Capoferro and Vincentio Saviolo.


title: Rapier

text: The rapier became extremely fashionable throughout Europe with the wealthier classes, but was not without its detractors. Some people, such as George Silver, disapproved of its technical potential and the dueling use to which it was put.


title: Rapier

text: Allowing for fast reactions, and with a long reach, the rapier was well suited to civilian combat in the 16th–17th centuries. As military-style cutting and thrusting swords continued to evolve to meet needs on the battlefield, so did the rapier continue to evolve to meet the needs of civilian combat and decorum, eventually becoming lighter, shorter and less cumbersome to wear. This is when the rapier began to give way to the colichemarde itself being later superseded by the small sword which was later superseded by the épée. Noticeably, there were some "war rapiers" that feature a relatively wide blade mounted on a typical rapier hilt during this era. These hybrid swords were used in the military or even in battlefield. Gustav II Adolf's carried a sword that was used in the Thirty Years' War and is a typical example of the "war rapier".


title: Rapier

text: By the year 1715, the rapier had been largely replaced by the lighter small sword throughout most of Europe, although the former continued to be used, as evidenced by the treatises of Donald McBane (1728), P. J. F. Girard (1736) and Domenico Angelo (1787). The rapier is still used today by officers of the Swiss Guard of the pope.


title: Rapier

text: Classical fencing schools claim to have inherited aspects of rapier forms in their systems. In 1885, fencing scholar Egerton Castle wrote "there is little doubt that the French system of fencing can be traced, at its origin, to the ancient Italian swordsmanship; the modern Italian school being of course derived in an uninterrupted manner from the same source." Castle went on to note that "the Italians have preserved the rapier form, with cup, pas d'ane, and quillons, but with a slender quadrangular blade."


title: Bristol Palin

text: Bristol Sheeran Marie Palin (born October 18, 1990) is an American public speaker, reality television personality, and real estate agent. She is the oldest daughter and second of five children of Todd and Sarah Palin.


title: Bristol Palin

text: Palin competed in the fall 2010 season of "Dancing with the Stars" and reached the finals, finishing in third place. In summer 2011, Palin released a memoir. In summer 2012, she starred in the Lifetime show "". Her most recent television series was as a member of the fall celebrity cast of "Dancing with the Stars"s 15th season in 2012, where she was eliminated in the fourth week of competition.


title: Bristol Palin

text: Palin was born in Wasilla, Alaska, to parents Todd and Sarah (née Heath) Palin. She was named "Bristol" for the Bristol Inn where her mother Sarah was employed; Bristol, Connecticut, the headquarters city of ESPN, where her mother Sarah hoped to work as a sportscaster; and the Bristol Bay area of Alaska, where her father Todd grew up. Her mother, Sarah, is of English, Irish, and German ancestry. Her father, Todd has Yup'ik (from a great-grandmother), Dutch, and English ancestry. Bristol is a Native American as a lineal descendant of her father Todd, who is a native enrollee under the 1970 Alaska Native Claims Settlement Act, making her a member of the Yup'ik tribe.


title: Bristol Palin

text: Palin was raised largely in Wasilla and attended Juneau-Douglas High School when her mother was governor of Alaska. During 2008, she briefly lived in Anchorage with her aunt and uncle where she attended West Anchorage High School. After returning to Wasilla, she attended and then graduated from Wasilla High School in May 2009.


title: Bristol Palin

text: Bristol Palin was first thrown into the national spotlight after Sen John McCain chose Sarah Palin to be his vice presidential running mate in late August 2008; his advisers had already been informed of her 17-year-old daughter Bristol's pregnancy, which they believed would be a political liability because the teen was unmarried. On September 1, 2008, the opening day of the 2008 Republican National Convention, it was publicly announced that Bristol Palin was pregnant and engaged to Levi Johnston, her baby's father. Palin's entire immediate family, along with Johnston, appeared at the convention.


title: Bristol Palin

text: McCain's advisers reportedly thought a wedding between Johnston and Palin would boost the waning popularity of the McCain-Palin ticket. Johnston denied claims that he was being pressured into a shotgun wedding, stating, "We were planning on getting married a long time ago with or without the kid. That was the plan from the start."


title: Bristol Palin

text: Palin first became the subject of media attention when her pregnancy was announced during her mother's Vice Presidential campaign. In February 2009, she told Fox News that abstinence is "not realistic at all," but that she would like it to become more accepted among people her age.


title: Bristol Palin

text: At age 18 in May 2009, Palin appeared on the "Today" show and "Good Morning America" in recognition of the National Day to Prevent Teen Pregnancy. She called for all teens to abstain from sex. Such observance was started by The National Campaign to Prevent Teen and Unplanned Pregnancy. Palin was not employed by the Campaign, nor was she a spokesperson for the organization. Palin said that her abstinence quote of February had been "taken out of context".


title: Bristol Palin

text: Also in May 2009, Palin was named a Teen Pregnancy Prevention Ambassador for the Candie's Foundation, a teen pregnancy prevention organization that is a division of the Candie's clothing brand. Her duties as a paid spokeswoman involved attending town hall meetings, talking about abstinence, public service announcements, and giving interviews on morning talk shows.


title: Bristol Palin

text: In September 2009, Palin formed BSMP, a lobbying, public relations and political consulting services firm. While the initial focus was to be work with Candie's Foundation, BSMP was planned to develop additional clients.


title: Bristol Palin

text: In May 2009, on "Good Morning America", Palin said, "Regardless of what I did personally, abstinence is the only 100% foolproof way you can prevent pregnancy." In an interview on "Good Morning America" in April 2010, she said that "'Pause Before You Play' [a campaign of Candie's] hits a wider range of message, it can mean pause and go get a condom, it can be pause and think about your life, or it could be pause and wait until marriage."


title: Bristol Palin

text: Her role as a spokesperson drew some public criticism. Bonnie Fuller, former editor-in-chief of "YM", questioned whether the net effect of Palin's public speaking had glamorized rather than discouraged teen pregnancy, noting that the "picture perfect" imagery of a "People" magazine spread seemed to make her "the poster girl for teen momhood". That same month, Meghan McCain stated her support for sex education, criticizing Palin's sexual abstinence campaign, saying it was "not realistic for this generation".


title: Bristol Palin

text: In April 2011 the media reported that Palin was paid more than $262,000 by Candie's Foundation for her work in 2009. This level of compensation, which constituted 12% of the foundation's annual budget, was criticized by some commentators as excessive.


title: Bristol Palin

text: In a July 10, 2011, interview with Drew Pinsky, Palin said she does not want to "be named as an abstinence preacher ... I'm not out there saying don't have sex. I hate that kind of stuff. Birth control needs to be used effectively each and every single time if you're gonna be having sex. ... I'm not advocating [abstinence] for everyone else."


title: Bristol Palin

text: On July 13, 2011, Palin had an interview with "Christianity Today" in which she reaffirmed her stance on abstinence. Discussing whether she still thought that abstinence was unrealistic, as she had said in 2009, she said "that quote was taken out of context. What I am trying to say is it's not realistic for everyone...but for me, my sisters, and my family, I believe that’s the right way." Palin still feels that abstinence is the only choice for her and her family.


title: Bristol Palin

text: In 2015, Bristol Palin took to her blog to correct the media regarding what the Candies Organization is and her role within it, stating, "Let's get another thing straight, because I can't tolerate all the talk on this subject. I have never been paid as an “abstinence spokesperson.” I was employed by the great people at The Candies Foundation. They are a teen pregnancy prevention non-profit and I worked for them when I was 18 and 19 — when I could share first hand the challenges of being a teen mother. I know you remember me most from when Mom ran for Vice President. However, I'm not 17 anymore, I am 24. I've been employed at the same doctor's office for over six years now; I own a home; I have a well-rounded, beautiful son. I am pregnant [with my second child.] This is not the ideal situation, but life is important even if it's not in the most absolute ideal circumstance. This is more confirmation on what I've always stood for. I've always been pro-life and I am standing for life now."


title: Bristol Palin

text: In May 2010, the media reported that Palin had signed with the company Single Source Speakers, asking between $15,000 and $30,000 for each appearance. She was listed on the company's website as available for conferences, fundraisers, special events and holidays, as well as women's, youth, abstinence, and pro-life programs.


title: Bristol Palin

text: In January 2011, Palin was invited to speak by Washington University in St. Louis as the keynote speaker for "Abstinence in College" at Sexual Responsibility Week. Students protested both the high fee she was to be paid out of student-generated funds and her lack of expertise on abstinence in college. Her appearance was cancelled.


title: Bristol Palin

text: Palin appeared in an episode of the ABC Family network series "The Secret Life of the American Teenager", playing a friend of the fictional character Amy, a 15-year-old who is dealing with an unexpected pregnancy. She filmed the scenes in Los Angeles in March 2010; the episode aired on July 5, 2010. "I like doing speaking engagements and stuff like that," she said, adding, "I don't think I'll be doing any more acting in the future."


title: Bristol Palin

text: Palin was a competitor on the fall 2010 season of "Dancing with the Stars". She was partnered with professional Mark Ballas, who had won with Olympic figure skater Kristi Yamaguchi in Season 6 and with Olympic gymnast Shawn Johnson in Season 8. The season was televised from September through November 2010.


title: Bristol Palin

text: Despite getting the lowest scores from the judges for a number of weeks, Palin and Ballas avoided being eliminated during the season. That attracted media attention and speculation. Questions were raised about the integrity of the public voting process including allegations of fraudulent online voting using multiple e-mail addresses. ABC executives and the show's executive producer, Conrad Green, said that "checks and balances" in the system, including IP-address verification, prevent such voting practices. Green said, "There's nothing in the voting that looks dissimilar to previous seasons". Nonetheless, Green speculated that Palin may have received votes from her mother's fans and other supporters, and from older viewers who had maternal feelings toward her due to her youth and lack of experience. Palin credited her success to the support of her fans who were tuning in each week to see her improvement.


title: Bristol Palin

text: Palin's success on the show attracted death threats and other negative attention. Suspicious white powder was sent to the show; it turned out to be harmless, but security on the show was tightened.


title: Bristol Palin

text: On the final show of the season, Palin and Ballas finished in third place. Before the show, Palin said that winning "would be like a big middle finger out there to all the people out there who hate my mom and hate me". Following the competition, she remarked that she was happy with her third-place finish, that prayer and faith had helped her, and that she had grown as a person.


title: Bristol Palin

text: In November 2010, Bristol Palin made an appearance on the TLC travelogue-documentary "Sarah Palin's Alaska." She helped the crew on a commercial halibut fishing boat.


title: Bristol Palin

text: In October 2010, while competing on "Dancing With the Stars" Season 11, Palin appeared in a music video for an Alaskan symphony rock band called Static Cycle. The video was shot at the Ice Museum in Chena Hot Springs, Alaska.


title: Bristol Palin

text: Palin's docu-series "Life's a Tripp", produced by Associated Television International, premiered on June 19, 2012, in the United States, on Lifetime TV. Lifetime ordered 14 episodes for original broadcast. The series followed Palin as she moved to Los Angeles, then back to Alaska, with two episodes set in Arizona (where her sister Willow was attending beauty school) and one episode in Washington, D.C.


title: Bristol Palin

text: Palin competed on the all-star Season 15 of "DWTS", which began in late September 2012. She was again partnered with Mark Ballas. The two were eliminated in week 4 of the season, in which they had the second-lowest score from the judges.


title: Bristol Palin

text: In July 2018, Bristol was cast in "Teen Mom OG" after Farrah Abraham's exit from the show. She quit in April 2019.


title: Bristol Palin

text: In July 2018, Palin began working as a real estate agent with Keller Williams Realty in Austin, Texas.


title: Bristol Palin

text: In late January 2020, Bristol joined local boutique real estate agency Austin Home Seekers to expand the Bristol Palin Team.


title: Bristol Palin

text: In June 2011, Palin's memoir, "Not Afraid of Life: My Journey So Far", co-authored by Nancy French, was released. In the book, Palin candidly discusses aspects of her personal life, including tensions with the McCain family and losing her virginity. The book received mixed reviews from critics and readers. It reached #21 on "The New York Times" Best Seller list for hardcover nonfiction.


title: Bristol Palin

text: In 2008, two months after her 18th birthday, Palin gave birth to her and Johnston's son. In response to the suggestion that it would have been more prudent to abort her pregnancy and that she only carried it to term because of her mother's views on the issue she responded: 'It doesn't matter what my mom's views are on it. It was my decision.'


title: Bristol Palin

text: Palin and Johnston ended their engagement in March 2009. In November 2009, a custody and child support case was filed in a local Alaska court. Palin asked the court to use pseudonyms for herself and Johnston to keep the normally public proceedings private, arguing that the media attention would not be good for the child. Johnston argued for open proceedings, as the power of the Palin family was relevant to the case, which he claimed he wanted to be decided on the merits, and that he did "not feel protected against Sarah Palin in a closed proceeding."


title: Bristol Palin

text: On December 27, 2009, the judge ruled in favor of Johnston, and it was publicly announced that the pair had been battling for legal custody. Palin tried to win full custody rights and child support consistent with Johnston's income, made statements that Johnston had "exercised sporadic visitation rights", and tried to present him as a bad father by speculating without offering evidence that he "wants the rights for his own self-promotion". Johnston sought shared custody and lower child support payments.


title: Bristol Palin

text: In February 2010, a judge ruled that Johnston had to pay back child support, with a hearing set to determine the amount of ongoing support payments.


title: Bristol Palin

text: That month, Palin and her son began living in a condo she had purchased in Anchorage, where she was working at a dermatologist's office and taking business courses at a community college. In July 2010, Palin and Johnston announced that they had reunited and were again engaged, but less than three weeks later, they ended their second engagement. The couple reached an agreement giving primary custody to Palin, and visitation rights and child support responsibility to Johnston.


title: Bristol Palin

text: On March 13, 2015, Palin announced she had become engaged to Dakota Meyer, a former Marine and Medal of Honor recipient. According to Bristol's blog, she first met Meyer in 2014 while filming "Amazing America" with her mother Sarah Palin in Alaska. On May 18, 2015, Palin's mother announced that the wedding planned for later in the week had been called off.


title: Bristol Palin

text: On June 25, 2015, Palin announced she was pregnant with her second child, and that the father was Meyer. In the announcement she stated the news would come as "a huge disappointment" to her friends and family but said she did not want any sympathy or lectures. Three days later she said that the pregnancy was "not the ideal situation" but was "planned." She said she would not consider abortion and her pregnancy was not in conflict with her work for the Candie's Foundation. She gave birth to a daughter in December 2015. In June 2016, Palin and Meyer married. In December 2016, Palin announced that she was expecting her third child, the second with Meyer. In 2017, she gave birth to a daughter.


title: Bristol Palin

text: On February 13, 2018, Palin and Meyer announced their separation and that Meyer had filed for divorce. Palin and Meyer battled on social media during the divorce. Meyer at one point shared a screenshot that Palin had sent to Sam Boyd (a motocross rider on the MTV reality show "Nitro Circus"), in which Palin called Meyer a coward, and said he did not deserve his Medal of Honor. On August 1, 2018, Palin confirmed that her divorce from Meyer had been finalized.


title: Bristol Palin

text: In December 2013, she spoke out in defense of "Duck Dynasty" star Phil Robertson following his disagreement with homosexuality based on his religious beliefs.


title: Bristol Palin

text: Palin opposed the 2015 name change from Mount McKinley to Denali. In a blog post, Palin wrote that "I’ve never called the mountain Denali .. and neither does anyone I know." Following her blog post, it was reported that her mother used the name Denali during her farewell speech when resigning from the governorship of Alaska.


title: Medication

text: A medication (also called medicament, medicine, pharmaceutical drug, medicinal drug or simply drug) is a drug used to diagnose, cure, treat, or prevent disease. Drug therapy (pharmacotherapy) is an important part of the medical field and relies on the science of pharmacology for continual advancement and on pharmacy for appropriate management.


title: Medication

text: Drugs are classified in multiple ways. One of the key divisions is by level of control, which distinguishes prescription drugs (those that a pharmacist dispenses only on the order of a physician, physician assistant, or qualified nurse) from over-the-counter drugs (those that consumers can order for themselves). Another key distinction is between traditional small molecule drugs, usually derived from chemical synthesis, and biopharmaceuticals, which include recombinant proteins, vaccines, blood products used therapeutically (such as IVIG), gene therapy, monoclonal antibodies and cell therapy (for instance, stem cell therapies). Other ways to classify medicines are by mode of action, route of administration, biological system affected, or therapeutic effects. An elaborate and widely used classification system is the Anatomical Therapeutic Chemical Classification System. The World Health Organization keeps a list of essential medicines.


title: Medication

text: Drug discovery and drug development are complex and expensive endeavors undertaken by pharmaceutical companies, academic scientists, and governments. As a result of this complex path from discovery to commercialization, partnering has become a standard practice for advancing drug candidates through development pipelines. Governments generally regulate what drugs can be marketed, how drugs are marketed, and in some jurisdictions, drug pricing. Controversies have arisen over drug pricing and disposal of used drugs.


title: Medication

text: Medication is a medicine or a chemical compound used to treat or cure illness. According to "Encyclopædia Britannica", medication is "a substance used in treating a disease or relieving pain".


title: Medication

text: As defined by the National Cancer Institute, dosage forms of medication can include tablets, capsules, liquids, creams, and patches. Medications can be given in different ways, such as by mouth, by infusion into a vein, or by drops put into the ear or eye. A medication that does not contain an active ingredient and is used in research studies is called a placebo.


title: Medication

text: Drug use among elderly Americans has been studied; in a group of 2377 people with average age of 71 surveyed between 2005 and 2006, 84% took at least one prescription drug, 44% took at least one over-the-counter (OTC) drug, and 52% took at least one dietary supplement; in a group of 2245 elderly Americans (average age of 71) surveyed over the period 2010 – 2011, those percentages were 88%, 38%, and 64%.


title: Medication

text: One of the key classifications is between traditional small molecule drugs; usually derived from chemical synthesis, and biologic medical products; which include recombinant proteins, vaccines, blood products used therapeutically (such as IVIG), gene therapy, and cell therapy (for instance, stem cell therapies).


title: Medication

text: Pharmaceuticals or drugs or medicines are classified in various other groups besides their origin on the basis of pharmacological properties like mode of action and their pharmacological action or activity, such as by chemical properties, mode or route of administration, biological system affected, or therapeutic effects. An elaborate and widely used classification system is the Anatomical Therapeutic Chemical Classification System (ATC system). The World Health Organization keeps a list of essential medicines.


title: Medication

text: Pharmaceuticals may also be described as "specialty", independent of other classifications, which is an ill-defined class of drugs that might be difficult to administer, require special handling during administration, require patient monitoring during and immediately after administration, have particular regulatory requirements restricting their use, and are generally expensive relative to other drugs.


title: Medication

text: Drugs affecting the central nervous system include: psychedelics, hypnotics, anaesthetics, antipsychotics, eugeroics, antidepressants (including tricyclic antidepressants, monoamine oxidase inhibitors, lithium salts, and selective serotonin reuptake inhibitors (SSRIs)), antiemetics, Anticonvulsants/antiepileptics, anxiolytics, barbiturates, movement disorder (e.g., Parkinson's disease) drugs, nootropics, stimulants (including amphetamines), benzodiazepines, cyclopyrrolones, dopamine antagonists, antihistamines, cholinergics, anticholinergics, emetics, cannabinoids, and 5-HT (serotonin) antagonists.


title: Medication

text: The main categories of drugs for musculoskeletal disorders are: NSAIDs (including COX-2 selective inhibitors), muscle relaxants, neuromuscular drugs, and anticholinesterases.


title: Medication

text: Antibiotics, sympathomimetics, antihistamines, anticholinergics, NSAIDs, corticosteroids, antiseptics, local anesthetics, antifungals, cerumenolytic.


title: Medication

text: Bronchodilators, antitussives, mucolytics, decongestants, inhaled and systemic corticosteroids, beta2-adrenergic agonists, anticholinergics, mast cell stabilizers, leukotriene antagonists.


title: Medication

text: Androgens, antiandrogens, estrogens, gonadotropin, corticosteroids, human growth hormone, insulin, antidiabetics (sulfonylureas, biguanides/metformin, thiazolidinediones, insulin), thyroid hormones, antithyroid drugs, calcitonin, diphosphonate, vasopressin analogues.


title: Medication

text: Antifungal, alkalinizing agents, quinolones, antibiotics, cholinergics, anticholinergics, antispasmodics, 5-alpha reductase inhibitor, selective alpha-1 blockers, sildenafils, fertility medications.


title: Medication

text: NSAIDs, anticholinergics, haemostatic drugs, antifibrinolytics, Hormone Replacement Therapy (HRT), bone regulators, beta-receptor agonists, follicle stimulating hormone, luteinising hormone, LHRH, gamolenic acid, gonadotropin release inhibitor, progestogen, dopamine agonists, oestrogen, prostaglandins, gonadorelin, clomiphene, tamoxifen, diethylstilbestrol.


title: Medication

text: Emollients, anti-pruritics, antifungals, antiseptics, scabicides, pediculicides, tar products, vitamin A derivatives, vitamin D analogues, keratolytics, abrasives, systemic antibiotics, topical antibiotics, hormones, desloughing agents, exudate absorbents, fibrinolytics, proteolytics, sunscreens, antiperspirants, corticosteroids, immune modulators.


title: Medication

text: Antibiotics, antifungals, antileprotics, antituberculous drugs, antimalarials, anthelmintics, amoebicides, antivirals, antiprotozoals, probiotics, prebiotics, antitoxins and antivenoms.


title: Medication

text: Tonics, electrolytes and mineral preparations (including iron preparations and magnesium preparations), parenteral nutritions, vitamins, anti-obesity drugs, anabolic drugs, haematopoietic drugs, food product drugs.


title: Medication

text: Cytotoxic drugs, therapeutic antibodies, sex hormones, aromatase inhibitors, somatostatin inhibitors, recombinant interleukins, G-CSF, erythropoietin.


title: Medication

text: A euthanaticum is used for euthanasia and physician-assisted suicide. Euthanasia is not permitted by law in many countries, and consequently, medicines will not be licensed for this use in those countries.


title: Medication

text: Administration is the process by which a patient takes a medicine. There are three major categories of drug administration: enteral (via the human gastrointestinal tract), injection into the body, and by other routes (dermal, nasal, ophthalmic, otologic, and urogenital).


title: Medication

text: Oral administration, the most common form of enteral administration, can be performed using various dosage forms including tablets or capsules and liquid such as a syrup or suspension. Other ways to take medication include buccally (placed inside cheek), sublingually (placed underneath tongue), eye and ear drops (dropped into eye or ear), and transdermally (applied to skin).


title: Medication

text: They can be administered in one dose, as a bolus. Administration frequencies are often abbreviated from Latin, such as "every 8 hours" reading Q8H from "Quaque VIII Hora". The drug frequencies are often expressed as the number of times a drug is used per day (e.g., four times a day). It may include event-related information (e.g., 1 hour before meals, in the morning, at bedtime), or complimentary to interval, although equivalent expressions may have different implications (e.g., every 8 hours versus 3 times a day).


title: Medication

text: In the fields of medicine, biotechnology and pharmacology, drug discovery is the process by which new drugs are discovered.


title: Medication

text: Historically, drugs were discovered through identifying the active ingredient from traditional remedies or by serendipitous discovery. Later chemical libraries of synthetic small molecules, natural products or extracts were screened in intact cells or whole organisms to identify substances that have a desirable therapeutic effect in a process known as classical pharmacology. Since sequencing of the human genome which allowed rapid cloning and synthesis of large quantities of purified proteins, it has become common practice to use high throughput screening of large compounds libraries against isolated biological targets which are hypothesized to be disease-modifying in a process known as reverse pharmacology. Hits from these screens are then tested in cells and then in animals for efficacy. Even more recently, scientists have been able to understand the shape of biological molecules at the atomic level, and to use that knowledge to design (see drug design) drug candidates.


title: Medication

text: Modern drug discovery involves the identification of screening hits, medicinal chemistry and optimization of those hits to increase the affinity, selectivity (to reduce the potential of side effects), efficacy/potency, metabolic stability (to increase the half-life), and oral bioavailability. Once a compound that fulfills all of these requirements has been identified, it will begin the process of drug development prior to clinical trials. One or more of these steps may, but not necessarily, involve computer-aided drug design.


title: Medication

text: Despite advances in technology and understanding of biological systems, drug discovery is still a lengthy, "expensive, difficult, and inefficient process" with low rate of new therapeutic discovery. In 2010, the research and development cost of each new molecular entity (NME) was approximately US$1.8 billion. Drug discovery is done by pharmaceutical companies, sometimes with research assistance from universities. The "final product" of drug discovery is a patent on the potential drug. The drug requires very expensive Phase I, II and III clinical trials, and most of them fail. Small companies have a critical role, often then selling the rights to larger companies that have the resources to run the clinical trials.


title: Medication

text: Drug discovery is different from Drug Development. Drug Discovery is often considered the process of identifying new medicine. At the same time, Drug development is delivering a new drug molecule into clinical practice. In its broad definition, this encompasses all steps from the basic research process of finding a suitable molecular target to supporting the drug's commercial launch.


title: Medication

text: Drug development is the process of bringing a new drug to the market once a lead compound has been identified through the process of drug discovery. It includes pre-clinical research (microorganisms/animals) and clinical trials (on humans) and may include the step of obtaining regulatory approval to market the drug.


title: Medication

text: Discovery: The Drug Development process starts with Discovery, a process of identifying a new medicine.


title: Medication

text: Development: Chemicals extracted from natural products are used to make pills, capsules, or syrups for oral use. Injections for direct infusion into the blood drops for eyes or ear.


title: Medication

text: Preclinical research : Drugs go under laboratory or animal testing, to ensure that they can be used on Humans.


title: Medication

text: FDA post Market Review: The drug is reviewed and monitored by FDA for the safety once it is available to the public


title: Medication

text: The regulation of drugs varies by jurisdiction. In some countries, such as the United States, they are regulated at the national level by a single agency. In other jurisdictions, they are regulated at the state level, or at both state and national levels by various bodies, as is the case in Australia. The role of therapeutic goods regulation is designed mainly to protect the health and safety of the population. Regulation is aimed at ensuring the safety, quality, and efficacy of the therapeutic goods which are covered under the scope of the regulation. In most jurisdictions, therapeutic goods must be registered before they are allowed to be marketed. There is usually some degree of restriction of the availability of certain therapeutic goods depending on their risk to consumers.


title: Medication

text: Depending upon the jurisdiction, drugs may be divided into over-the-counter drugs (OTC) which may be available without special restrictions, and prescription drugs, which must be prescribed by a licensed medical practitioner in accordance with medical guidelines due to the risk of adverse effects and contraindications. The precise distinction between OTC and prescription depends on the legal jurisdiction. A third category, "behind-the-counter" drugs, is implemented in some jurisdictions. These do not require a prescription, but must be kept in the dispensary, not visible to the public, and be sold only by a pharmacist or pharmacy technician. Doctors may also prescribe prescription drugs for off-label use – purposes which the drugs were not originally approved for by the regulatory agency. The Classification of Pharmaco-Therapeutic Referrals helps guide the referral process between pharmacists and doctors.


title: Medication

text: The International Narcotics Control Board of the United Nations imposes a world law of prohibition of certain drugs. They publish a lengthy list of chemicals and plants whose trade and consumption (where applicable) is forbidden. OTC drugs are sold without restriction as they are considered safe enough that most people will not hurt themselves accidentally by taking it as instructed. Many countries, such as the United Kingdom have a third category of "pharmacy medicines", which can be sold only in registered pharmacies by or under the supervision of a pharmacist.


title: Medication

text: Medical errors include over prescription and polypharmacy, mis-prescription, contraindication and lack of detail in dosage and administrations instructions. In 2000 the definition of a prescription error was studied using a Delphi method conference; the conference was motivated by ambiguity in the what a prescription error and a need to use a uniform definition in studies.


title: Medication

text: In the UK, the Pharmaceutical Price Regulation Scheme is intended to ensure that the National Health Service is able to purchase drugs at reasonable prices. The prices are negotiated between the Department of Health, acting with the authority of Northern Ireland and the UK Government, and the representatives of the Pharmaceutical industry brands, the Association of the British Pharmaceutical Industry (ABPI). For 2017 this payment percentage set by the PPRS will be 4,75%.


title: Medication

text: In Canada, the Patented Medicine Prices Review Board examines drug pricing and determines if a price is excessive or not. In these circumstances, drug manufacturers must submit a proposed price to the appropriate regulatory agency. Furthermore, "the International Therapeutic Class Comparison Test is responsible for comparing the National Average Transaction Price of the patented drug product under review" different countries that the prices are being compared to are the following: France, Germany, Italy, Sweden, Switzerland, the United Kingdom, and the United States


title: Medication

text: In Brazil, the prices are regulated through a legislation under the name of "Medicamento Genérico" (generic drugs) since 1999.


title: Medication

text: In the United States, drug costs are partially unregulated, but instead are the result of negotiations between drug companies and insurance companies.


title: Medication

text: High prices have been attributed to monopolies given to manufacturers by the government. New drug development costs continue to rise as well. Despite the enormous advances in science and technology, the number of new blockbuster drugs approved by the government per billion dollars spent has halved every 9 years since 1950.


title: Medication

text: A blockbuster drug is a drug that generates more than $1 billion in revenue for a pharmaceutical company in a single year. Cimetidine was the first drug ever to reach more than $1 billion a year in sales, thus making it the first blockbuster drug.


title: Medication

text: Antibiotics first arrived on the medical scene in 1932 thanks to Gerhard Domagk; and were coined the "wonder drugs". The introduction of the sulfa drugs led to the mortality rate from pneumonia in the U.S. to drop from 0.2% each year to 0.05% by 1939. Antibiotics inhibit the growth or the metabolic activities of bacteria and other microorganisms by a chemical substance of microbial origin. Penicillin, introduced a few years later, provided a broader spectrum of activity compared to sulfa drugs and reduced side effects. Streptomycin, found in 1942, proved to be the first drug effective against the cause of tuberculosis and also came to be the best known of a long series of important antibiotics. A second generation of antibiotics was introduced in the 1940s: aureomycin and chloramphenicol. Aureomycin was the best known of the second generation.


title: Medication

text: Lithium was discovered in the 19th century for nervous disorders and its possible mood-stabilizing or prophylactic effect; it was cheap and easily produced. As lithium fell out of favor in France, valpromide came into play. This antibiotic was the origin of the drug that eventually created the mood stabilizer category. Valpromide had distinct psychotrophic effects that were of benefit in both the treatment of acute manic states and in the maintenance treatment of manic depression illness. Psychotropics can either be sedative or stimulant; sedatives aim at damping down the extremes of behavior. Stimulants aim at restoring normality by increasing tone. Soon arose the notion of a tranquilizer which was quite different from any sedative or stimulant. The term tranquilizer took over the notions of sedatives and became the dominant term in the West through the 1980s. In Japan, during this time, the term tranquilizer produced the notion of a psyche-stabilizer and the term mood stabilizer vanished.


title: Medication

text: Premarin (conjugated estrogens, introduced in 1942) and Prempro (a combination estrogen-progestin pill, introduced in 1995) dominated the hormone replacement therapy (HRT) during the 1990s. HRT is not a life-saving drug, nor does it cure any disease. HRT has been prescribed to improve one's quality of life. Doctors prescribe estrogen for their older female patients both to treat short-term menopausal symptoms and to prevent long-term diseases. In the 1960s and early 1970s, more and more physicians began to prescribe estrogen for their female patients. between 1991 and 1999, Premarin was listed as the most popular prescription and best-selling drug in America.


title: Medication

text: The first oral contraceptive, Enovid, was approved by FDA in 1960. Oral contraceptives inhibit ovulation and so prevent conception. Enovid was known to be much more effective than alternatives including the condom and the diaphragm. As early as 1960, oral contraceptives were available in several different strengths by every manufacturer. In the 1980s and 1990s, an increasing number of options arose including, most recently, a new delivery system for the oral contraceptive via a transdermal patch. In 1982, a new version of the Pill was introduced, known as the "biphasic" pill. By 1985, a new triphasic pill was approved. Physicians began to think of the Pill as an excellent means of birth control for young women.


title: Medication

text: Stimulants such as Ritalin (methylphenidate) came to be pervasive tools for behavior management and modification in young children. Ritalin was first marketed in 1955 for narcolepsy; its potential users were middle-aged and the elderly. It wasn't until some time in the 1980s along with hyperactivity in children that Ritalin came onto the market. Medical use of methlyphenidate is predominantly for symptoms of attention deficit/hyperactivity disorder (ADHD). Consumption of methylphenidate in the U.S. out-paced all other countries between 1991 and 1999. Significant growth in consumption was also evident in Canada, New Zealand, Australia, and Norway. Currently, 85% of the world's methylphenidate is consumed in America.


title: Medication

text: The first minor tranquilizer was Meprobamate. Only fourteen months after it was made available, meprobamate had become the country's largest-selling prescription drug. By 1957, meprobamate had become the fastest-growing drug in history. The popularity of meprobamate paved the way for Librium and Valium, two minor tranquilizers that belonged to a new chemical class of drugs called the benzodiazepines. These were drugs that worked chiefly as anti-anxiety agents and muscle relaxants. The first benzodiazepine was Librium. Three months after it was approved, Librium had become the most prescribed tranquilizer in the nation. Three years later, Valium hit the shelves and was ten times more effective as a muscle relaxant and anti-convulsant. Valium was the most versatile of the minor tranquilizers. Later came the widespread adoption of major tranquilizers such as chlorpromazine and the drug reserpine. In 1970, sales began to decline for Valium and Librium, but sales of new and improved tranquilizers, such as Xanax, introduced in 1981 for the newly created diagnosis of panic disorder, soared.


title: Medication

text: Mevacor (lovastatin) is the first and most influential statin in the American market. The 1991 launch of Pravachol (pravastatin), the second available in the United States, and the release of Zocor (simvastatin) made Mevacor no longer the only statin on the market.


title: Medication

text: Using plants and plant substances to treat all kinds of diseases and medical conditions is believed to date back to prehistoric medicine.


title: Medication

text: The Kahun Gynaecological Papyrus, the oldest known medical text of any kind, dates to about 1800 BC and represents the first documented use of any kind of drug. It and other medical papyri describe Ancient Egyptian medical practices, such as using honey to treat infections and the legs of bee-eaters to treat neck pains.


title: Medication

text: Ancient Babylonian medicine demonstrated the use of medication in the first half of the 2nd millennium BC. Medicinal creams and pills were employed as treatments.


title: Medication

text: On the Indian subcontinent, the Atharvaveda, a sacred text of Hinduism whose core dates from the second millennium BC, although the hymns recorded in it are believed to be older, is the first Indic text dealing with medicine. It describes plant-based drugs to counter diseases. The earliest foundations of ayurveda were built on a synthesis of selected ancient herbal practices, together with a massive addition of theoretical conceptualizations, new nosologies and new therapies dating from about 400 BC onwards. The student of Āyurveda was expected to know ten arts that were indispensable in the preparation and application of his medicines: distillation, operative skills, cooking, horticulture, metallurgy, sugar manufacture, pharmacy, analysis and separation of minerals, compounding of metals, and preparation of alkalis.


title: Medication

text: The Hippocratic Oath for physicians, attributed to fifth century BC Greece, refers to the existence of "deadly drugs", and ancient Greek physicians imported drugs from Egypt and elsewhere. The pharmacopoeia "De materia medica," written between 50 and 70 CE by the Greek physician Pedanius Dioscorides, was widely read for more than 1,500 years.


title: Medication

text: Al-Kindi's ninth century AD book, "De Gradibus" and Ibn Sina (Avicenna)'s "The Canon of Medicine", covers a range of drugs known to the practice of medicine in the medieval Islamic world.


title: Medication

text: Medieval medicine of Western Europe saw advances in surgery compared to previously, but few truly effective drugs existed, beyond opium (found in such extremely popular drugs as the "Great Rest" of the Antidotarium Nicolai at the time) and quinine. Folklore cures and potentially poisonous metal-based compounds were popular treatments. Theodoric Borgognoni, (1205–1296), one of the most significant surgeons of the medieval period, responsible for introducing and promoting important surgical advances including basic antiseptic practice and the use of anaesthetics. Garcia de Orta described some herbal treatments that were used.


title: Medication

text: For most of the 19th century, drugs were not highly effective, leading Oliver Wendell Holmes, Sr. to famously comment in 1842 that "if all medicines in the world were thrown into the sea, it would be all the better for mankind and all the worse for the fishes".


title: Medication

text: During the First World War, Alexis Carrel and Henry Dakin developed the Carrel-Dakin method of treating wounds with an irrigation, Dakin's solution, a germicide which helped prevent gangrene.


title: Medication

text: In the inter-war period, the first anti-bacterial agents such as the sulpha antibiotics were developed. The Second World War saw the introduction of widespread and effective antimicrobial therapy with the development and mass production of penicillin antibiotics, made possible by the pressures of the war and the collaboration of British scientists with the American pharmaceutical industry.


title: Medication

text: Medicines commonly used by the late 1920s included aspirin, codeine, and morphine for pain; digitalis, nitroglycerin, and quinine for heart disorders, and insulin for diabetes. Other drugs included antitoxins, a few biological vaccines, and a few synthetic drugs. In the 1930s, antibiotics emerged: first sulfa drugs, then penicillin and other antibiotics. Drugs increasingly became "the center of medical practice". In the 1950s, other drugs emerged including corticosteroids for inflammation, rauvolfia alkaloids as tranquilizers and antihypertensives, antihistamines for nasal allergies, xanthines for asthma, and typical antipsychotics for psychosis. As of 2007, thousands of approved drugs have been developed. Increasingly, biotechnology is used to discover biopharmaceuticals. Recently, multi-disciplinary approaches have yielded a wealth of new data on the development of novel antibiotics and antibacterials and on the use of biological agents for antibacterial therapy.


title: Medication

text: In the 1950s, new psychiatric drugs, notably the antipsychotic chlorpromazine, were designed in laboratories and slowly came into preferred use. Although often accepted as an advance in some ways, there was some opposition, due to serious adverse effects such as tardive dyskinesia. Patients often opposed psychiatry and refused or stopped taking the drugs when not subject to psychiatric control.


title: Medication

text: Governments have been heavily involved in the regulation of drug development and drug sales. In the U.S., the Elixir Sulfanilamide disaster led to the establishment of the Food and Drug Administration, and the 1938 Federal Food, Drug, and Cosmetic Act required manufacturers to file new drugs with the FDA. The 1951 Humphrey-Durham Amendment required certain drugs to be sold by prescription. In 1962, a subsequent amendment required new drugs to be tested for efficacy and safety in clinical trials.


title: Medication

text: Until the 1970s, drug prices were not a major concern for doctors and patients. As more drugs became prescribed for chronic illnesses, however, costs became burdensome, and by the 1970s nearly every U.S. state required or encouraged the substitution of generic drugs for higher-priced brand names. This also led to the 2006 U.S. law, Medicare Part D, which offers Medicare coverage for drugs.


title: Medication

text: As of 2008, the United States is the leader in medical research, including pharmaceutical development. U.S. drug prices are among the highest in the world, and drug innovation is correspondingly high. In 2000, U.S.-based firms developed 29 of the 75 top-selling drugs; firms from the second-largest market, Japan, developed eight, and the United Kingdom contributed 10. France, which imposes price controls, developed three. Throughout the 1990s, outcomes were similar.


title: Medication

text: Controversies concerning pharmaceutical drugs include patient access to drugs under development and not yet approved, pricing, and environmental issues.


title: Medication

text: Governments worldwide have created provisions for granting access to drugs prior to approval for patients who have exhausted all alternative treatment options and do not match clinical trial entry criteria. Often grouped under the labels of compassionate use, expanded access, or named patient supply, these programs are governed by rules which vary by country defining access criteria, data collection, promotion, and control of drug distribution.


title: Medication

text: Within the United States, pre-approval demand is generally met through treatment IND (investigational new drug) applications (INDs), or single-patient INDs. These mechanisms, which fall under the label of expanded access programs, provide access to drugs for groups of patients or individuals residing in the US. Outside the US, Named Patient Programs provide controlled, pre-approval access to drugs in response to requests by physicians on behalf of specific, or "named", patients before those medicines are licensed in the patient's home country. Through these programs, patients are able to access drugs in late-stage clinical trials or approved in other countries for a genuine, unmet medical need, before those drugs have been licensed in the patient's home country.


title: Medication

text: Patients who have not been able to get access to drugs in development have organized and advocated for greater access. In the United States, ACT UP formed in the 1980s, and eventually formed its Treatment Action Group in part to pressure the US government to put more resources into discovering treatments for AIDS and then to speed release of drugs that were under development.


title: Medication

text: The Abigail Alliance was established in November 2001 by Frank Burroughs in memory of his daughter, Abigail. The Alliance seeks broader availability of investigational drugs on behalf of terminally ill patients.


title: Medication

text: In 2013, BioMarin Pharmaceutical was at the center of a high-profile debate regarding expanded access of cancer patients to experimental drugs.


title: Medication

text: Essential medicines, as defined by the World Health Organization (WHO), are "those drugs that satisfy the health care needs of the majority of the population; they should therefore be available at all times in adequate amounts and in appropriate dosage forms, at a price the community can afford." Recent studies have found that most of the medicines on the WHO essential medicines list, outside of the field of HIV drugs, are not patented in the developing world, and that lack of widespread access to these medicines arise from issues fundamental to economic development – lack of infrastructure and poverty. Médecins Sans Frontières also runs a Campaign for Access to Essential Medicines campaign, which includes advocacy for greater resources to be devoted to currently untreatable diseases that primarily occur in the developing world. The Access to Medicine Index tracks how well pharmaceutical companies make their products available in the developing world.


title: Medication

text: World Trade Organization negotiations in the 1990s, including the TRIPS Agreement and the Doha Declaration, have centered on issues at the intersection of international trade in pharmaceuticals and intellectual property rights, with developed world nations seeking strong intellectual property rights to protect investments made to develop new drugs, and developing world nations seeking to promote their generic pharmaceuticals industries and their ability to make medicine available to their people via compulsory licenses.


title: Medication

text: Some have raised ethical objections specifically with respect to pharmaceutical patents and the high prices for drugs that they enable their proprietors to charge, which poor people around the world, cannot afford. Critics also question the rationale that exclusive patent rights and the resulting high prices are required for pharmaceutical companies to recoup the large investments needed for research and development. One study concluded that marketing expenditures for new drugs often doubled the amount that was allocated for research and development. Other critics claim that patent settlements would be costly for consumers, the health care system, and state and federal governments because it would result in delaying access to lower cost generic medicines.


title: Medication

text: Novartis fought a protracted battle with the government of India over the patenting of its drug, Gleevec, in India, which ended up in a Supreme Court in a case known as Novartis v. Union of India & Others. The Supreme Court ruled narrowly against Novartis, but opponents of patenting drugs claimed it as a major victory.


title: Medication

text: The environmental impact of pharmaceuticals and personal care products is controversial. PPCPs are substances used by individuals for personal health or cosmetic reasons and the products used by agribusiness to boost growth or health of livestock. PPCPs comprise a diverse collection of thousands of chemical substances, including prescription and over-the-counter therapeutic drugs, veterinary drugs, fragrances, and cosmetics. PPCPs have been detected in water bodies throughout the world and ones that persist in the environment are called Environmental Persistent Pharmaceutical Pollutants. The effects of these chemicals on humans and the environment are not yet known, but to date there is no scientific evidence that they affect human health.


title: Exponentiation

text: Exponentiation is a mathematical operation, written as , involving two numbers, the "base" and the "exponent" or "power" , and pronounced as " (raised) to the (power of) ". When is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, is the product of multiplying bases:


title: Exponentiation

text: The exponent is usually shown as a superscript to the right of the base. In that case, is called ""b" raised to the "n"th power", ""b" (raised) to the power of "n"", "the "n"th power of "b"", ""b" to the "n"th power", or most briefly as ""b" to the "n"th".


title: Exponentiation

text: Starting from the basic fact stated above that, for any positive integer formula_2, formula_3 is formula_2 occurrences of formula_5 all multiplied by each other, several other properties of exponentiation directly follow. In particular:


title: Exponentiation

text: In other words, when multiplying a base raised to one exponent by the same base raised to another exponent, the exponents add. From this basic rule that exponents add, we can derive that formula_7 must be equal to 1, as follows. For any formula_2, formula_9. Dividing both sides by formula_3 gives formula_11.


title: Exponentiation

text: The fact that formula_12 can similarly be derived from the same rule. For example, formula_13. Taking the cube root of both sides gives formula_12.


title: Exponentiation

text: The rule that multiplying makes exponents add can also be used to derive the properties of negative integer exponents. Consider the question of what formula_15 should mean. In order to respect the "exponents add" rule, it must be the case that formula_16. Dividing both sides by formula_17 gives formula_18, which can be more simply written as formula_19, using the result from above that formula_12. By a similar argument, formula_21.


title: Exponentiation

text: The properties of fractional exponents also follow from the same rule. For example, suppose we consider formula_22 and ask if there is some suitable exponent, which we may call formula_23, such that formula_24. From the definition of the square root, we have that formula_25. Therefore, the exponent formula_23 must be such that formula_27. Using the fact that multiplying makes exponents add gives formula_28. The formula_29 on the right-hand side can also be written as formula_30, giving formula_31. Equating the exponents on both sides, we have formula_32. Therefore, formula_33, so formula_34.


title: Exponentiation

text: The definition of exponentiation can be extended to allow any real or complex exponent. Exponentiation by integer exponents can also be defined for a wide variety of algebraic structures, including matrices.


title: Exponentiation

text: Exponentiation is used extensively in many fields, including economics, biology, chemistry, physics, and computer science, with applications such as compound interest, population growth, chemical reaction kinetics, wave behavior, and public-key cryptography.


title: Exponentiation

text: The term "power" () is a mistranslation of the ancient Greek δύναμις ("dúnamis", here: "amplification") used by the Greek mathematician Euclid for the square of a line, following Hippocrates of Chios. In "The Sand Reckoner", Archimedes discovered and proved the law of exponents, , necessary to manipulate powers of . In the 9th century, the Persian mathematician Muhammad ibn Mūsā al-Khwārizmī used the terms مَال ("māl", "possessions", "property") for a square—the Muslims, "like most mathematicians of those and earlier times, thought of a squared number as a depiction of an area, especially of land, hence property"—and كَعْبَة ("kaʿbah", "cube") for a cube, which later Islamic mathematicians represented in mathematical notation as the letters "mīm" (m) and "kāf" (k), respectively, by the 15th century, as seen in the work of Abū al-Hasan ibn Alī al-Qalasādī.


title: Exponentiation

text: Nicolas Chuquet used a form of exponential notation in the 15th century, which was later used by Henricus Grammateus and Michael Stifel in the 16th century. The word "exponent" was coined in 1544 by Michael Stifel. Samuel Jeake introduced the term "indices" in 1696. In the 16th century, Robert Recorde used the terms square, cube, zenzizenzic (fourth power), sursolid (fifth), zenzicube (sixth), second sursolid (seventh), and zenzizenzizenzic (eighth). "Biquadrate" has been used to refer to the fourth power as well.


title: Exponentiation

text: Early in the 17th century, the first form of our modern exponential notation was introduced by René Descartes in his text titled "La Géométrie"; there, the notation is introduced in Book I.


title: Exponentiation

text: Some mathematicians (such as Isaac Newton) used exponents only for powers greater than two, preferring to represent squares as repeated multiplication. Thus they would write polynomials, for example, as .


title: Exponentiation

text: Another historical synonym, involution, is now rare and should not be confused with its more common meaning.


title: Exponentiation

text: In 1748, Leonhard Euler introduced variable exponents, and, implicitly, non-integer exponents by writing:


title: Exponentiation

text: The expression is called "the square of "b"" or ""b" squared", because the area of a square with side-length is .


title: Exponentiation

text: Similarly, the expression is called "the cube of "b"" or ""b" cubed", because the volume of a cube with side-length is .


title: Exponentiation

text: When it is a positive integer, the exponent indicates how many copies of the base are multiplied together. For example, . The base appears times in the multiplication, because the exponent is . Here, is the "5th power of 3", or "3 raised to the 5th power".


title: Exponentiation

text: The word "raised" is usually omitted, and sometimes "power" as well, so can be simply read "3 to the 5th", or "3 to the 5". Therefore, the exponentiation can be expressed as ""b" to the power of "n"", ""b" to the "n"th power", ""b" to the "n"th", or most briefly as ""b" to the "n"".


title: Exponentiation

text: A formula with nested exponentiation, such as (which means and not ), is called a tower of powers, or simply a tower.


title: Exponentiation

text: The exponentiation operation with integer exponents may be defined directly from elementary arithmetic operations.


title: Exponentiation

text: The definition of the exponentiation as an iterated multiplication can be formalized by using induction, and this definition can be used as soon one has an associative multiplication:


title: Exponentiation

text: to zero exponents. It may be used in every algebraic structure with a multiplication that has an identity.


title: Exponentiation

text: Intuitionally, formula_7 may be interpreted as the empty product of copies of . So, the equality formula_42 is a special case of the general convention for the empty product.


title: Exponentiation

text: The case of is more complicated. In contexts where only integer powers are considered, the value is generally assigned to formula_43 but, otherwise, the choice of whether to assign it a value and what value to assign may depend on context.


title: Exponentiation

text: Exponentiation with negative exponents is defined by the following identity, which holds for any integer and nonzero :


title: Exponentiation

text: Raising 0 to a negative exponent is undefined but, in some circumstances, it may be interpreted as infinity (formula_45).


title: Exponentiation

text: This definition of exponentiation with negative exponents is the only one that allows extending the identity formula_40 to negative exponents (consider the case formula_47).


title: Exponentiation

text: The same definition applies to invertible elements in a multiplicative monoid, that is, an algebraic structure, with an associative multiplication and a multiplicative identity denoted (for example, the square matrices of a given dimension). In particular, in such a structure, the inverse of an invertible element is standardly denoted formula_48


title: Exponentiation

text: The following identities, often called , hold for all integer exponents, provided that the base is non-zero:


title: Exponentiation

text: Unlike addition and multiplication, exponentiation is not commutative. For example, . Also unlike addition and multiplication, exponentiation is not associative. For example, , whereas . Without parentheses, the conventional order of operations for serial exponentiation in superscript notation is top-down (or "right"-associative), not bottom-up (or "left"-associative). That is,


title: Exponentiation

text: However, this formula is true only if the summands commute (i.e. that ), which is implied if they belong to a structure that is commutative. Otherwise, if and are, say, square matrices of the same size, this formula cannot be used. It follows that in computer algebra, many algorithms involving integer exponents must be changed when the exponentiation bases do not commute. Some general purpose computer algebra systems use a different notation (sometimes instead of ) for exponentiation with non-commuting bases, which is then called non-commutative exponentiation.


title: Exponentiation

text: For nonnegative integers and , the value of is the number of functions from a set of elements to a set of elements (see cardinal exponentiation). Such functions can be represented as -tuples from an -element set (or as -letter words from an -letter alphabet). Some examples for particular values of and are given in the following table:


title: Exponentiation

text: In the base ten (decimal) number system, integer powers of are written as the digit followed or preceded by a number of zeroes determined by the sign and magnitude of the exponent. For example, and .


title: Exponentiation

text: Exponentiation with base is used in scientific notation to denote large or small numbers. For instance, (the speed of light in vacuum, in metres per second) can be written as and then approximated as .


title: Exponentiation

text: SI prefixes based on powers of are also used to describe small or large quantities. For example, the prefix kilo means , so a kilometre is .


title: Exponentiation

text: Powers of appear in set theory, since a set with members has a power set, the set of all of its subsets, which has members.


title: Exponentiation

text: Integer powers of are important in computer science. The positive integer powers give the number of possible values for an -bit integer binary number; for example, a byte may take different values. The binary number system expresses any number as a sum of powers of , and denotes it as a sequence of and , separated by a binary point, where indicates a power of that appears in the sum; the exponent is determined by the place of this : the nonnegative exponents are the rank of the on the left of the point (starting from ), and the negative exponents are determined by the rank on the right of the point.


title: Exponentiation

text: If the exponent is negative (), the th power of zero is undefined, because it must equal formula_54 with , and this would be formula_55 according to above.


title: Exponentiation

text: Because of this, powers of are useful for expressing alternating sequences. For a similar discussion of powers of the complex number , see .


title: Exponentiation

text: The limit of a sequence of powers of a number greater than one diverges; in other words, the sequence grows without bound:


title: Exponentiation

text: This can be read as ""b" to the power of "n" tends to +∞ as "n" tends to infinity when "b" is greater than one".


title: Exponentiation

text: Powers of alternate between and as alternates between even and odd, and thus do not tend to any limit as grows.


title: Exponentiation

text: If , alternates between larger and larger positive and negative numbers as alternates between even and odd, and thus does not tend to any limit as grows.


title: Exponentiation

text: If the exponentiated number varies while tending to as the exponent tends to infinity, then the limit is not necessarily one of those above. A particularly important case is


title: Exponentiation

text: Other limits, in particular those of expressions that take on an indeterminate form, are described in below.


title: Exponentiation

text: Real functions of the form formula_56, where formula_57, are sometimes called power functions. When formula_2 is an integer and formula_59, two primary families exist: for formula_2 even, and for formula_2 odd. In general for formula_62, when formula_2 is even formula_56 will tend towards positive infinity with increasing formula_65, and also towards positive infinity with decreasing formula_65. All graphs from the family of even power functions have the general shape of formula_67, flattening more in the middle as formula_2 increases. Functions with this kind of symmetry are called even functions.


title: Exponentiation

text: When formula_2 is odd, formula_70's asymptotic behavior reverses from positive formula_65 to negative formula_65. For formula_62, formula_56 will also tend towards positive infinity with increasing formula_65, but towards negative infinity with decreasing formula_65. All graphs from the family of odd power functions have the general shape of formula_77, flattening more in the middle as formula_2 increases and losing all flatness there in the straight line for formula_79. Functions with this kind of symmetry are called odd functions.


title: Exponentiation

text: If is a nonnegative real number, and is a positive integer, formula_81 or formula_82 denotes the unique positive real th root of , that is, the unique positive real number such that formula_83


title: Exponentiation

text: If is a positive real number, and formula_84 is a rational number, with and integers, then formula_85 is defined as


title: Exponentiation

text: On the other hand, there are problems with the extension of these definitions to bases that are not positive real numbers. For example, a negative real number has a real th root, which is negative, if is odd, and no real root if is even. In the latter case, whichever complex th root one chooses for formula_91 the identity formula_92 cannot be satisfied. For example,


title: Exponentiation

text: For positive real numbers, exponentiation to real powers can be defined in two equivalent ways, either by extending the rational powers to reals by continuity (, below), or in terms of the logarithm of the base and the exponential function (, below). The result is always a positive real number, and the identities and properties shown above for integer exponents remain true with these definitions for real exponents. The second definition is more commonly used, since it generalizes straightforwardly to complex exponents.


title: Exponentiation

text: On the other hand, exponentiation to a real power of a negative real number is much more difficult to define consistently, as it may be non-real and have several values (see ). One may choose one of these values, called the principal value, but there is no choice of the principal value for which the identity


title: Exponentiation

text: is true; see . Therefore, exponentiation with a basis that is not a positive real number is generally viewed as a multivalued function.


title: Exponentiation

text: Since any irrational number can be expressed as the limit of a sequence of rational numbers, exponentiation of a positive real number with an arbitrary real exponent can be defined by continuity with the rule


title: Exponentiation

text: where the limit is taken over rational values of only. This limit exists for every positive and every real .


title: Exponentiation

text: For example, if , the non-terminating decimal representation and the monotonicity of the rational powers can be used to obtain intervals bounded by rational powers that are as small as desired, and must contain formula_96


title: Exponentiation

text: So, the upper bounds and the lower bounds of the intervals form two sequences that have the same limit, denoted formula_98


title: Exponentiation

text: This defines formula_99 for every positive and real as a continuous function of and . See also Well-defined expression.


title: Exponentiation

text: The "exponential function" is often defined as formula_100 where formula_101 is Euler's number. For avoiding circular reasoning, this definition cannot be used here. So, a definition of the exponential function, denoted formula_102 and of Euler's number are given, which rely only on exponentiation with positive integer exponents. Then a proof is sketched that, if one uses the definition of exponentiation given in preceding sections, one has


title: Exponentiation

text: Euler's number can be defined as formula_110. It follows from the preceding equations that formula_111 when is an integer (this results from the repeated-multiplication definition of the exponentiation). If is real, formula_111 results from the definitions given in preceding sections, by using the exponential identity if is rational, and the continuity of the exponential function otherwise.


title: Exponentiation

text: The limit that defines the exponential function converges for every complex value of , and therefore it can be used to extend the definition of formula_113, and thus formula_114 from the real numbers to any complex argument . This extended exponential function still satisfies the exponential identity, and is commonly used for defining exponentiation for complex base and exponent.


title: Exponentiation

text: The definition of as the exponential function allows defining for every positive real numbers , in terms of exponential and logarithm function. Specifically, the fact that the natural logarithm is the inverse of the exponential function means that one has