Final answer:
If a star's temperature goes up by a factor of 4, its luminosity would change by a factor of 256 according to the Stefan-Boltzmann law.
Step-by-step explanation:
The luminosity of a star is related to its temperature through the Stefan-Boltzmann law, which states that the luminosity is proportional to the fourth power of the temperature.
If the temperature of a star increases by a factor of 4, the luminosity would increase by a factor of 4^4, which is 256.
Therefore, the star's luminosity would change by a factor of 256 if its temperature goes up by a factor of 4.