Final answer:
The last area of Muslim expansion included the region of India, leading to the establishment of the Delhi Sultanate in the twelfth century, which expanded Islam's influence and facilitated cultural interchange through its robust participation in Indian Ocean trade.
Step-by-step explanation:
The last area of Muslim expansion included the region of India, specifically the formation of the Delhi Sultanate. The Muslim presence in India was a result of invasions that began in the eighth century, eventually leading to the establishment of the Delhi Sultanate in 1206. This period of expansion saw the conversion of many locals to Islam, strengthening the religion's influence in the region and creating a critical link in Indian Ocean trade. The Delhi Sultanate defended itself against Mongol invasions and expanded significantly, ultimately governing a vast territory and facilitating further conversions to Islam through various policies and the region's social dynamics.
Different dynasties within India, including the Chalukyas in Gujarat and the eventual rise of the Mughal Empire, illustrate the complex interchange between local Indian traditions and the pervasive influence of Islam. Muslim traders also played an essential role in the expansion of Islamic culture through their dominance in the Indian Ocean maritime trade, which extended all the way to China and included significant cultural exchange.