Final answer:
The Muslim empire in Persia is the Safavid Empire, the one in Anatolia is the Ottoman Empire, and the Hindu empire in India is the Mughal Empire. The Almoravid option is not used.
Step-by-step explanation:
The student is asking to match historical descriptions to their corresponding empires. For clarity, here are the matches:
- Muslim empire in Persia that followed the Shia branch of Islam; expanded their trade and obtained new inventions like gunpowder and muskets; Persian rugs, art, architecture, and literature flourished: This description matches the Safavid Empire.
- Muslim empire in Anatolia that followed the Sunni branch of Islam; were at war with the Persian empire because they wanted their land and did not approve of their leader's treatment of the Sunni citizens: This description refers to the Ottoman Empire.
- Hindu empire in India, begun by Babur – a Muslim; he made alliances with Hindu princes and allowed them to practice their religion freely: This description fits the Mughal Empire.
The Almoravid dynasty is not mentioned in the given descriptions and thus will not be used.