(A) Execute - carry out or put into effect (a plan, order, or course of action)
(B) Expanse - an area of something, typically land or sea, presenting a wide continuous surface
(C) Academic - relating to education and scholarship/ not of practical relevance; of only theoretical interest/ related to knowledge
(D) Settle - resolve or reach an agreement about (an argument or problem).
The given word Erudite means having or showing great knowledge or learning. From the given explanations of the options, option (C) is most synonymous to the given word. Hence the answer is option (C).