Which of the following powers does an administrative agency NOT possess?

The correct choice reflects a fundamental aspect of administrative agencies and their powers. Administrative agencies are established to enforce and interpret laws, and they have a variety of powers, including investigatory powers, rule-making authority, and enforcement capabilities. However, the term "nonappealable adjudicatory powers" suggests that the decisions made by these agencies cannot be appealed, which is not accurate.

In practice, the decisions made by administrative agencies can often be challenged and appealed in court. There is typically a legal framework permitting parties affected by an agency's decision to contest it, ensuring that there is a system of checks and balances. Thus, while agencies exercise significant authority in their adjudicative functions, the outcomes of those adjudications are generally subject to judicial review, making "nonappealable adjudicatory powers" inconsistent with the actual legal structure surrounding administrative law. This underlines why this option is the correct answer; it misrepresents the reality of administrative agency powers in terms of appealability.