Why do you think the eastern half of the empire survived

Because of the organization and capable leadership of the empire.

Explanation:

Byzantium did not survive by "mere luck." Byzantium has maintained thanks to capable leaders, an organization, skilled diplomats and an excellent military organization. True, he did not possess "that splendour" as the Western Roman Empire at its height, but it is wrong to think that thanks to luck, the empire was maintained for almost a thousand years after the fall of the Western Roman Empire. The great French Byzantologist and historian Charles Diehl says "The Byzantine Empire was a captive of Christianity in the east, against the unbelievers it saved Europe in a few moments by its inferiority, in the Middle Ages ".

1st and 3rd : ) now lemme smash

d: their own individual powers within the new goverment