{"status": "success", "data": {"description_md": "Given that $3^8\\cdot5^2=a^b,$ where both $a$ and $b$ are positive integers, find the smallest possible value for $a+b$.\n\n$\\textbf{(A) } 25 \\qquad\\textbf{(B) } 34 \\qquad\\textbf{(C) } 351 \\qquad\\textbf{(D) } 407 \\qquad\\textbf{(E) } 900$", "description_html": "<p>Given that  <span class=\"katex--inline\">3^8\\cdot5^2=a^b,</span>  where both  <span class=\"katex--inline\">a</span>  and  <span class=\"katex--inline\">b</span>  are positive integers, find the smallest possible value for  <span class=\"katex--inline\">a+b</span> .</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) } 25 \\qquad\\textbf{(B) } 34 \\qquad\\textbf{(C) } 351 \\qquad\\textbf{(D) } 407 \\qquad\\textbf{(E) } 900</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": "2003 AMC 10B Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/03_amc10B_p15", "prev": "/problem/03_amc10B_p13"}}