Question

active galactic nuclei (agn) are powered by
nuclear reactions.
hypernovae.
rapid star formation.
matter falling into the supermassive black hole at the center of a galaxy.

Explanation:

Active galactic nuclei (AGN) are powered by the gravitational - potential energy released as matter falls into the supermassive black hole at the center of a galaxy. Nuclear reactions power stars, hypernovae are explosive events of massive stars, and rapid star - formation is related to star - birth regions, not the power source of AGN.

Answer:

matter falling into the supermassive black hole at the center of a galaxy.