Question

the extent of the Byzantine territory at the height of its power

Answer 1

The Byzantine empire reached its physical height under the reign of Justinian I. This map below shows the full extent of the empire under his reign:

http://faculty.cbhs.org/jward/Maps/byzantine%20empire%20map.jpg

It nearly encompassed all of the lands once held by the Roman Empire, but much of that would eventually be lost in the years following Justinian's death. His hold over those territories was marginal at best,

Answer 2

and welcome to open study! :D