Final answer:
Athens as the hegemon of the Delian League exercised the greatest degree of power through the influence of its highest-ranking officials and its ability to intimidate and patronize smaller states.
Step-by-step explanation:
Athens as the hegemon of the Delian League exercised the greatest degree of power. This was due to several factors. Firstly, all of the highest-ranking officials of the League were Athenian, such as Aristides and Cimon. Secondly, Athens had the ability to influence policy and strategy through intimidation and patronage of smaller states.