# Basic Algebra/Introduction to Basic Algebra Ideas/Exponents and Powers
## Vocabulary
### Exponent

    A number written in superscript that denotes how many times the base will be multiplied by itself.

### Base (or radix)

    The number to be multiplied by itself.
Example: $5^{2}=25$
In this example, the base is 5 and the exponent is 2.

## Lesson

We use exponents to show when we're multiplying the same number more than one time.

### $3\times 3=3^{2}$

    Three times three equals three to the second power (or three squared)

### $3\times 3\times 3=3^{3}$

    Three times three times three equals three to the third power (or three cubed)

### $3\times 3\times 3\times 3=3^{4}$

    Three times three times three times three equal three to the fourth power

### $2\times 2\times 2=2^{3}$

    Two times two times two equals two to the third power
Note that any nonzero number raised to the 0 power is always equal to 1.

### $2^{0}=1$

    Two to the zero power equals one
We can also raise any number to a negative exponent. This is called the inverse exponent and places the number on the bottom of a fraction with a 1 on top:

### $2^{-2}={\frac {1}{2^{2}}}={\frac {1}{4}}$

    Two to the negative two equals one over two to the second power

## Example Problems

Let's evaluate these expressions.
* $7^{2}$
| $7\times 7$ | Seven to the second power, or seven squared, means seven times seven. |
| $49$ | Seven times seven is forty-nine. |
    Seven to the second power equals forty-nine.
* What is the area of a square with a side of 3 meters length?
| Area = (length of the side)$^2$ | The area, or space inside, of a square is equal to the length of the side of the square to the second power. |
| (3 meters)$^2$ | The length of the side is 3 meters, so the area is (3 meters) squared. |
| $3\times 3$ meters$^2$ | 3 squared is the same as 3 times 3. |
| 9 square meters | Three times three is nine. |
    So, the area of a square with a side length of 3 meters is 9 square meters.
* $c^{2}$ where $c=6$
| $6^{2}$ | First, we replace the variable "c" in the expression with 6, which is what it equals. |
| $6\times 6$ | 6 squared equals 6 times 6. |
| $36$ | 6 times 6 equals 36. |
    So, c squared is 36.
* $x^{3}$ where $x=10$.
| $10^{3}$ | First, we replace the variable "x" in the expression with 10, which is what it equals. |
| $10\times 10\times 10$ | 10 to the third power, or 10 cubed, is equal to 10 times 10 times 10. |
| $100\times 10$ | 10 times 10 equals 100. |
| $1000$ | 100 times 10 equals 1000. |
    So, x to the third power is 1000.
* $y^{4}$ where $y=2$
| $2^{4}$ | First, we replace the variable "y" in the expression with 2, which is what it equals. |
| $2\times 2\times 2\times 2$ | 2 to the fourth power is equal to 2 times 2 times 2 times 2. |
| $4\times 2\times 2$ | 2 times 2 equals 4. |
| $8\times 2$ | 4 times 2 equals 8. |
| $16$ | And 8 times 2 equals 16. |
    So, y to the fourth is 16.
* $3^{-3}$
| ${\frac {1}{3^{3}}}$ | Three to the negative third power, which can be expressed as 1 over three cubed. |
| ${\frac {1}{27}}$ | Three cubed equals 3 times 3 times 3 which equals 27. |
    So, three to the negative third power equals one twenty-seventh.

## Practice Games

* http://www.math.com/school/subject2/practice/S2U2L2/S2U2L2Pract.html
* http://www.quia.com/pop/50485.html (scientific notation)
* http://www.softschools.com/math/games/exponents_practice.jsp
* http://www.quia.com/quiz/358716.html (King Kong Scientific Notation)
* http://www.shodor.org/interactivate/activities/OrderOfOperationsFou/ (order of operations including exponents)

## Practice Problems

Use / as the fraction line!