Question: Who was this Mughal Emperor that reigned nearly half a century whom Saadat Ali Khan I fought alongside with against the Maratha in the Deccan?
Context: The Battle of Purandar was fought between the Mughal Empire and Maratha Empire in 1665.  The Mughal Emperor, Aurangzeb, sent his generals Dilir Khan and Jai Singh to besiege Shivaji's fortress at Purandar.  After Mughal forces killed Maratha General Murar Baji Prabhu on June 2nd, 1665, Shivaji surrendered and gave up 23 of his fortresses.  Most of the fortresses were later recaptured by Marathas. Muhi-ud-Din Muhammad (3 November 1618 – 3 March 1707), commonly known by the sobriquet Aurangzeb (Persian: "Ornament of the Throne") or by his regnal title Alamgir (Persian: "Conqueror of the World"), was the sixth, and widely considered the last effective Mughal emperor.  His reign lasted for 49 years from 1658 until his death in 1707. The Mughal–Maratha Wars were fought between the Maratha Empire and the Mughal Empire from 1680 to 1707.  The Deccan Wars started in 1680 with the Mughal emperor Aurangzeb’s invasion of the Maratha enclave in Bijapur established by Shivaji. Muhammad Ali Khan Wallajah, or Muhammad Ali Khan Walla Jah (7 July 1717 – 13 October 1795), was the Nawab of Arcot in India and an ally of the British East India Company.  Muhammad Ali Khan Wallajah was born to Anwaruddin Muhammed Khan, by his second wife, "Fakhr un-nisa Begum Sahiba", was a niece of Sayyid Ali Khan Safavi ul-Mosawi of Persia, sometime Naib suba of Trichonopoly, on 7 July 1717 at Delhi.  Muhammed Ali Khan Wallajah the Nawab of Arcot often referred to himself as the Subedar of the Carnatic in his letters and correspondence with the then Mughal Emperor Shah Alam II. Saadat Ali Khan (b. c. 1680 – d. 19 March 1739) was the Subahdar Nawab of Awadh (Oudh) from 26 January 1722 to 1739, and the son of Muhammad Nasir.  At the age of 25 he accompanied his father Muhammad Nasir and joined the final campaign of the Mughal Emperor Aurangzeb against the Maratha in the Deccan, where the Mughal Emperor honorably awarded him the title "Khan Bahadur" for his steadfast services. Abu'l-Fath Jalal-ud-din Muhammad Akbar (15 October 1542 – 27 October 1605), popularly known as Akbar I (, literally "the great") and later Akbar the Great, was the third Mughal emperor, who reigned from 1556 to 1605.  Akbar succeeded his father, Humayun, under a regent, Bairam Khan, who helped the young emperor expand and consolidate Mughal domains in India.  A strong personality and a successful general, Akbar gradually enlarged the Mughal Empire to include nearly all of the Indian Subcontinent north of the Godavari river.  His power and influence, however, extended over the entire country because of Mughal military, political, cultural, and economic dominance.  To unify the vast Mughal state, Akbar established a centralised system of administration throughout his empire and adopted a policy of conciliating conquered rulers through marriage and diplomacy.  To preserve peace and order in a religiously and culturally diverse empire, he adopted policies that won him the support of his non-Muslim subjects.  Eschewing tribal bonds and Islamic state identity, Akbar strove to unite far-flung lands of his realm through loyalty, expressed through an Indo-Persian culture, to himself as an emperor who had near-divine status. The earliest reference made to Fyzabad or now Faizabad is said to be in the Ramayana, in which the city is referred to as Saket, the mythical private estate of King Dashrath, father of Lord Ram but the other sources indicate that Saket, which means Heaven in Sanskrit, is the ancient name of holy city of Ayodhya not Faizabad.  However, more accurately, the reference is found in Medieval and Modern history, when Nawab Saadat Ali Khan, Burhan-ul-Mulk was given the charge of the Subah of Awadh around 1722 by the Mughal Court.  Nawab Sa'adat Khan made the first settlements along the banks of Ghaghra with a cantonment consisting of a fortress and mud barracks.  Due to these temporary dwellings, Faizabad was first known as 'Bangla' (implied meaning- hutment). The Battle of Alegaon was fought between Nizam Ali Khan of Hyderabad and Raghunathrao of the Maratha Empire against Madhavrao I of the Maratha Empire.  Raghunathrao had established an alliance with Nizam Ali Khan of Hyderabad.  When conflict arose between Raghunathrao and Madhavrao I, a joint campaign between Nizam Ali Khan and Raghunathrao resulted in Madhavrao I being heavily defeated.  Madhavrao I surrendered on November 12, 1762.  Nizam Ali Khan got all of his previously lost territories that were lost at the Battle of Udgir.  Madhavrao I submitted to his uncle, Raghunathrao. Ali Dost Khan, often referred to as Dost Ali Khan, was the Mughal Empire's Nawab of the Carnatic from 1732 to 1740.  He was the son of Ghulam Ali Khan, brother of the Nawab Saadatullah Khan.  His childless uncle adopted him as heir, and he succeeded his uncle in 1732, he successfully gained the investiture and an official Firman by the Mughal Emperor Muhammad Shah. The Siege of Jinji, (September, 1690–January 8, 1698), began when the Mughal Emperor Aurangzeb appointed Zulfiqar Ali Khan as the Nawab of the Carnatic and dispatched him to besiege and capture Jinji Fort, which had been sacked and captured by Maratha Empire troops led by Rajaram, they had also ambushed and killed about 300 Mughal Sowars in the Carnatic.  The Mughal Emperor Aurangzeb then ordered Ghazi ud-Din Khan Feroze Jung I to protect the supply routes leading to Jinji Fort and to support and provide reinforcements to Zulfiqar Ali Khan when needed.
Answer: Emperor Aurangzeb