Assuming that we can measure the apparent brightness of a star, what does the inverse square law of light allow us to do?

This law allows us to know how the illuminance  of the star varies with the square of the distance.

Explanation:

The Law of the Inverse of the Square for light, allows us to determine, in the case of a star, and considering it as a point source, how its illuminance  

 (power per unit area) varies with the square of the distance   that separates us from it when measuring its apparent brightness.

This law is expressed as follows:

Where is the pointance (The flux power per unit solid angle, which is somehow analog with the intensity).

As we can see, as the distance from the light source increases, the illuminance decreases.