Final answer:
The papacy and Charlemagne cooperated closely, with the former crowning the latter as Emperor and both benefiting from mutual support and legitimacy which aided in maintaining power during the early Middle Ages. The possible option will be A. They often needed eacher other's help in order to maintain power.
Step-by-step explanation:
The relationship between the papacy and Charlemagne during the early Middle Ages is best described as cooperative, where they often needed each other's help in order to maintain power. This partnership was evident when Pope Leo III crowned Charlemagne as the Holy Roman Emperor in 800 AD, which was beneficial for both parties: Charlemagne received the legitimacy of being recognized by the church while the papacy enjoyed the protection and support of a strong secular ruler.
Moreover, this alliance was strategic for the papacy in its quest to exercise greater influence in Western Europe, independent of the Byzantine Empire. The church also worked with new rulers to help legitimize their rule and Christianize their populations, further emphasizing the collaborative nature of the relationship between the papacy and the ruling class, exemplified by the interactions with Charlemagne.