{"status": "success", "data": {"description_md": "There are integers $a$, $b$, and $c$, each greater than 1, such that$$\\sqrt[a]{N \\sqrt[b]{N \\sqrt[c]{N}}} = \\sqrt[36]{N^{25}}$$for all $N > 1$. What is $b$?\n\n$\\textbf{(A)}\\ 2\\qquad\\textbf{(B)}\\ 3\\qquad\\textbf{(C)}\\ 4\\qquad\\textbf{(D)}\\ 5\\qquad\\textbf{(E)}\\ 6$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>There are integers  <span class=\"katex--inline\">a</span> ,  <span class=\"katex--inline\">b</span> , and  <span class=\"katex--inline\">c</span> , each greater than 1, such that <span class=\"katex--display\">\\sqrt[a]{N \\sqrt[b]{N \\sqrt[c]{N}}} = \\sqrt[36]{N^{25}}</span> for all  <span class=\"katex--inline\">N &gt; 1</span> . What is  <span class=\"katex--inline\">b</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 2\\qquad\\textbf{(B)}\\ 3\\qquad\\textbf{(C)}\\ 4\\qquad\\textbf{(D)}\\ 5\\qquad\\textbf{(E)}\\ 6</span> </p>&#10;<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": "2020 AMC 12A Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/20_amc12A_p14", "prev": "/problem/20_amc12A_p12"}}