>>27.
Shit, I mean m^n, and most likely n >= 1, not m. But then well fuck I forgot half the problem already.
Anyway, the proof involves expanding n! into (n)(n - 1)(n - 2)...(2)(1), and expanding m^n into (m)(m)(m)(m)...(m) n times. Since it's a quotient, you have to show that the whole thing expands into (n / m) * ((n-1)/m) * ((n - 2)/m) *... (1/m) for n terms.
Well, this would have been clever if I had remembered exactly what I was talking about before I typed it all out. Sorry.