{"status": "success", "data": {"description_md": "Ted mistakenly wrote $2^m\\cdot\\sqrt{\\frac{1}{4096}}$ as $2\\cdot\\sqrt[m]{\\frac{1}{4096}}.$ What is the sum of all real numbers $m$ for which these two expressions have the same value?\n\n$\\textbf{(A) } 5 \\qquad \\textbf{(B) } 6 \\qquad \\textbf{(C) } 7 \\qquad \\textbf{(D) } 8 \\qquad \\textbf{(E) } 9$", "description_html": "<p>Ted mistakenly wrote  <span class=\"katex--inline\">2^m\\cdot\\sqrt{\\frac{1}{4096}}</span>  as  <span class=\"katex--inline\">2\\cdot\\sqrt[m]{\\frac{1}{4096}}.</span>  What is the sum of all real numbers  <span class=\"katex--inline\">m</span>  for which these two expressions have the same value?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) } 5 \\qquad \\textbf{(B) } 6 \\qquad \\textbf{(C) } 7 \\qquad \\textbf{(D) } 8 \\qquad \\textbf{(E) } 9</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": "2022 AMC 10A Problem 11", "can_next": true, "can_prev": true, "nxt": "/problem/22_amc10A_p12", "prev": "/problem/22_amc10A_p10"}}