Final answer:
If a star's temperature doubles and its radius decreases by a factor of 2, its luminosity would change by a factor of 4.
Step-by-step explanation:
The luminosity of a star is directly proportional to its temperature to the power of four and its radius squared. Therefore, if the star's temperature doubles, the luminosity would increase by a factor of 2^4 = 16. On the other hand, if the star's radius decreases by a factor of 2, the luminosity would decrease by a factor of (1/2)^2 = 1/4. Consequently, the combined effect of the temperature increase and radius decrease would cause the star's luminosity to change by a factor of 16 * (1/4) = 4.