Apparently this is simple, but I'm not seeing it.

P, A are matrices, n is a real.

Use induction to prove that $\displaystyle (P^{-1}AP)^n = P^{-1}A^nP$.

Presumably the first step is:

$\displaystyle (P^{-1}AP)^n = P^{-n}A^nP^n$

I'm not sure what's next, or if that is correct.