{"status": "success", "data": {"description_md": "Suppose that $P = 2^m$ and $Q = 3^n$. Which of the following is equal to $12^{mn}$ for every pair of integers $(m,n)$?\n\n$\\mathrm{(A)}\\ P^2Q\n\\qquad\n\\mathrm{(B)}\\ P^nQ^m\n\\qquad\n\\mathrm{(C)}\\ P^nQ^{2m}\n\\qquad\n\\mathrm{(D)}\\ P^{2m}Q^n\n\\qquad\n\\mathrm{(E)}\\ P^{2n}Q^m$", "description_html": "<p>Suppose that  <span class=\"katex--inline\">P = 2^m</span>  and  <span class=\"katex--inline\">Q = 3^n</span> . Which of the following is equal to  <span class=\"katex--inline\">12^{mn}</span>  for every pair of integers  <span class=\"katex--inline\">(m,n)</span> ?</p>\n<p> <span class=\"katex--inline\">\\mathrm{(A)}\\ P^2Q\n\\qquad\n\\mathrm{(B)}\\ P^nQ^m\n\\qquad\n\\mathrm{(C)}\\ P^nQ^{2m}\n\\qquad\n\\mathrm{(D)}\\ P^{2m}Q^n\n\\qquad\n\\mathrm{(E)}\\ P^{2n}Q^m</span> </p>\n<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2009 AMC 10A Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/09_amc10A_p14", "prev": "/problem/09_amc10A_p12"}}