Final answer:
The Mughal emperors showed their power through patronage of the arts, lavish architecture, and military conquests.
Step-by-step explanation:
The Mughal emperors showed their power in various ways. One of the key ways was through patronage of the arts. They supported artists and encouraged the study of plants, animals, and people. The court was a center of artistic excellence, and artists were able to sign their names and develop their own styles. The Mughal emperors also displayed their wealth and power through lavish architecture and extravagant displays of authority, such as the Peacock Throne and the Koh-i-Noor diamond. Additionally, they expanded the boundaries of the Mughal state through military conquests.