Final answer:
The Eastern Roman Empire remained stable and avoided the problems of the west due to its wealth, fewer barbarian incursions, the less powerful nobility, and more manageable geographic frontiers.
Step-by-step explanation:
The Eastern Empire was spared from many of the problems that plagued the west due to several reasons.
Firstly, the Eastern Empire, which included the Byzantine Empire, was much wealthier, with a strong and efficient bureaucracy and tax system that resulted in more revenue, amounting to roughly 270,000 pounds of gold annually, compared to the 20,000 pounds collected by the Western Empire.
This wealth allowed for better-equipped and trained armies in the east.
Secondly, the Eastern Roman Empire was geographically luckier than the west, with fewer barbarian incursions. The initial Gothic uprisings in the Balkans were redirected towards the west, and invasions that followed, including those by the Huns, were aimed at the Western Empire.
Furthermore, while the formidable Persian Empire posed a significant threat, there was a sustained period without major Persian invasions throughout the fifth century.
Finally, the administrative efficiency and less powerful nobility in the east also contributed to its survival. In contrast, the west dealt with incredibly powerful Roman elites who often undermined imperial authority and financial stability.
Geography also played a role; the east had a shorter frontier along the Danube River to defend and was more successful in managing relations with outside groups through diplomacy and wealth.