Final answer:
Both the Abbasid Caliphate and the Byzantine Empire struggled with internal power disputes and external pressures that led to their a. decline.
Step-by-step explanation:
The challenge that both the Abbasid Caliphate and the Byzantine Empire faced was a struggle with powerful internal actors seeking to exploit the weaknesses of their respective governments. This internal friction was amplified by external pressures such as loss of territory and economic downturn in the case of the Byzantine Empire, and political devolution and fragmentation for the Abbasid Caliphate. These challenges contributed to the decline of both empires, but they did not specifically face challenges like Mongol invasions or the development of writing systems to record scriptures as a common issue during the height of their respective powers. Economic decline and religious unrest were indeed faced by both, but civil war was not commonly reported as an internal challenge that both empires met simultaneously.
The Abbasid Caliphate and the Byzantine Empire both experienced religious unrest during their respective periods of power. While the Abbasid Caliphate faced challenges from rival caliphates and internal conflicts among different Islamic factions, the Byzantine Empire dealt with invasions from Persians and Arabs, resulting in the loss of territory and economic downturn. These religious tensions and conflicts significantly impacted the stability and unity of both empires.