Final answer:
Charlemagne's establishment of the Carolingian Empire was influenced by his alliance with the popes, the Carolingian Renaissance, and his reorganization of the Church. These factors played a significant role in the formation of his empire.
Step-by-step explanation:
Charlemagne's establishment of the Carolingian Empire was influenced by multiple factors. One key factor was his alliance with the popes, which allowed him to work independently of the Byzantine Empire and further his desire to conquer new territory and revive the idea of empire. Additionally, Charlemagne's empire was a reflection of the Carolingian Renaissance, which aimed to revive classical culture and learning. Lastly, Charlemagne's reorganization of the Church and his efforts to reform Church training and education, known as the "Carolingian Renaissance," were important contributions to the establishment of the Carolingian Empire.