I have absolutely no idea what the answer is ...

describe the role of nuclear fusion in the life cycle of a star and what happens when nuclear fusion in a star's core stops.

Nuclear fusion occurs in the core of a star. Stars use the process of nuclear fusion to convert hydrogen to helium, and this process provides energy for the star, making the star very hot and bright. When the star runs out of either hydrogen or helium and nuclear fusion in a star's core stops, the star is no longer creating energy. Without energy, the core cools and the outer layers of the star begin to expand and become less bright, and the star will eventually either collapse or explode.