Final answer:
By 850, the Islamic Empires had extended from Spain and the Maghreb in the west to the Indus River Valley in the east, spanning modern-day Pakistan and northern India, becoming the largest empire the world had seen at that time.
Step-by-step explanation:
By 850, the Islamic Empires had expanded dramatically since their beginnings in 634. After defeating the Byzantines and the Persians, they carved out an empire that stretched vastly in multiple directions. In the west, they reached as far as Spain and the Maghreb, which includes modern-day countries such as Morocco, Algeria, and Tunisia. To the east, the Islamic Empire's influence extended all the way to the Indus River Valley, spanning regions that are now parts of modern-day Pakistan and northern India.
These remarkable conquests made the Islamic Empire the largest that the world had seen up until that time, surpassing the realms of Alexander the Great, the Romans, and the Han Chinese. This vast territory was ruled by a caliph, establishing a powerful and culturally rich caliphate. The empire's eastern frontier was defined by its reach to the Mogul Empire of Pakistan and northern India, areas that later became deeply influenced by Islamic culture and leadership, as seen in the rule of Emperor Shah Jehan who built the Taj Mahal.