Prove that if you could observe the disks of stars through a telescope, you would notice that their surface brightness

Prove that if you could observe the disks of stars through a telescope, you would notice that their surface brightness is determined only by the temperature of the star’s surface.

The luminosity of a star is proportional to R ^ 2T ^ 4, where R and T are its radius and temperature. The brightness of a star on Earth is proportional to R ^ 2T ^ 4 / L ^ 2, where L is the distance to the star. The area of the visible disk is proportional to R ^ 2 / L ^ 2 As a result, the brightness per unit of the visible area is proportional to T ^ 4.