What happened?

nobody was powerful enough to reunify China under a single emperor

Explanation:

When the Han Dynasty collapsed in 220 CE, no one was powerful enough to reunify China under a single emperor. The result was the period of the Three Kingdoms, which lasted until 280 CE, when the Jin Dynasty took over. These three kingdoms, Wei, Shu, and Wu, battled for control in a long series of wars.

the factors that the economies of the muslim empires prosper were:

1- land trade routes-located between three continents  

2- sea trade routes

trade contributed to the spread of muslim empires, and with that islamic culture led to a growing feeling of internationalism resulted in the transfer of technology, science, and other cultural forms.