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2009 AMC 12A Question 6

AMC12 · 2009 AMC 12A

Question 6

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