Arguments for the powers used in the Lennard Jones Potential

grep6

Can anyone offer an explanation for the powers (6 and 12) used in the Lennard Jones potential? (other than simply saying weak attractive and strong repulsion forces)

I am especially looking for short derivation that can be used to argue that the attractive potential falls off with the sixth power of interatomic distance.

Also, I understand that the repulsive part is used as a convenient way to mimic an exponential. How do we go from the Pauli exclusion principle to an exponential barrier?

Thanks