Final answer:
The longest and most stable part of a star's life is known as the Main Sequence.
Step-by-step explanation:
The longest and most stable part of a star's life occurs once nuclear fusion begins. This phase is known as the Main Sequence. Once a star has reached the main-sequence stage, it derives its energy almost entirely from the conversion of hydrogen to helium via the process of nuclear fusion in its core. This process can maintain the star's equilibrium for a long time, and thus, all stars remain on the main sequence for most of their lives.