Question

How did the Inca most likely manage to rule such a vast mountain empire

Answer 1

They built a complex messaging system
<span />

Answer 2

Hello!

The Inca Empire was a vast empire that flourished in the Andean region of South America from the early 15th century, up until its conquest by the Spanish in the 1530s. They managed because they built their empire without wheel, powerful draft animals, iron working, currency or even what we would consider to be a writing system. To support this empire, a system of roads streteched for almost 25,000 miles , about three times the diameter of the Earth.

I hope you found this to be helpful! :)