Final answer:
The causes of the downfall of the Mongol rule in Persia and China were related to economic instability, internal rebellions, political conflicts, and military defeats.
Step-by-step explanation:
The downfall of Mongol rule in Persia and China had different causes. In Persia, external invasions and internal rebellions played a significant role, while China's downfall was primarily due to political conflicts and leadership issues. Both regions also faced economic instability and military defeats. However, it's important to note that trade decline was not a specific cause of the downfall in China, and cultural conflicts were not a significant factor in Persia.