Final answer:
The underlined pronoun 'themselves' in the given sentence is in the objective case because it is the object of the preposition 'among'.
Step-by-step explanation:
The underlined pronoun 'themselves' in the sentence 'They should have divided the duties more equally among themselves' is in the objective case.
An objective pronoun is used as the object of a verb or preposition. In this sentence, 'themselves' is the object of the preposition 'among'. The pronoun 'themselves' refers back to the noun 'They', indicating that they divided the duties among themselves.
Example: They should have divided the duties more equally among themselves, but they didn't.
Learn more about pronouns