Question

Why can't we get a picture of the lunar rover sitting on the surface of the moon with earth-based telescopes?

Answer 1

Telescopes have a property called resolving power.

Explanation:

This is the property of telescopes to separate two close objects.
To separate 100 meter object at lunar distance we need aperture about 1.9 meters.
So to separate rover which may be 2 meters we need telescope with aperture approximately 100 meters..