Where did Roman rule continue after the original Roman Empire fell?

Over time, the east thrived, while the west declined. In fact, after the western part of the Roman Empire fell, the eastern half continued to exist as the Byzantine Empire for hundreds of years. Therefore, the "fall of Rome" really refers only to the fall of the western half of the Empire.

Explanation:

what are local authorities doing to fix the problem

explanation: what are local authorities doing to fix the problem

i believe the answer would be 1.