Question

what happens first when a star begins to run out of fuel? the stars core shrinks. the star becomes a black hole. the star becomes a white dwarf. the stars outer layer drifts away.

Explanation:

When a star runs out of fuel, the core's gravitational pull causes it to shrink first. Becoming a black hole or white dwarf is a later stage. The outer layer drifting away (like in a planetary nebula) also occurs after core - related changes.

Answer:

The star's core shrinks.