{"status": "success", "data": {"description_md": "Real numbers $a$ and $b$ satisfy the equations $3^{a} = 81^{b + 2}$ and $125^{b} = 5^{a - 3}$. What is $ab$?\n\n$\\text{(A)}\\ -60 \\qquad \\text{(B)}\\ -17 \\qquad \\text{(C)}\\ 9 \\qquad \\text{(D)}\\ 12 \\qquad \\text{(E)}\\ 60$", "description_html": "<p>Real numbers  <span class=\"katex--inline\">a</span>  and  <span class=\"katex--inline\">b</span>  satisfy the equations  <span class=\"katex--inline\">3^{a} = 81^{b + 2}</span>  and  <span class=\"katex--inline\">125^{b} = 5^{a - 3}</span> . What is  <span class=\"katex--inline\">ab</span> ?</p>\n<p> <span class=\"katex--inline\">\\text{(A)}\\ -60 \\qquad \\text{(B)}\\ -17 \\qquad \\text{(C)}\\ 9 \\qquad \\text{(D)}\\ 12 \\qquad \\text{(E)}\\ 60</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": 1, "problem_name": "2007 AMC 10A Problem 9", "can_next": true, "can_prev": true, "nxt": "/problem/07_amc10A_p10", "prev": "/problem/07_amc10A_p08"}}