AMC 12 2009a Problem 6

Suppose that $P = 2^m$ and $Q = 3^n$. Which of the following is equal to $12^{mn}$ for every pair of integers $(m,n)$?

\textbf{(A)}\ P^2Q \textbf{(B)}\ P^nQ^m \textbf{(C)}\ P^nQ^{2m} \textbf{(D)}\ P^{2m}Q^n \textbf{(E)}\ P^{2n}Q^m