{"status": "success", "data": {"description_md": "The infinite product\n\n$$\\sqrt[3]{10} \\cdot \\sqrt[3]{\\sqrt[3]{10}} \\cdot \\sqrt[3]{\\sqrt[3]{\\sqrt[3]{10}}} \\cdots$$<br>evaluates to a real number. What is that number?\n\n$\\textbf{(A) }\\sqrt{10}\\qquad\\textbf{(B) }\\sqrt[3]{100}\\qquad\\textbf{(C) }\\sqrt[4]{1000}\\qquad\\textbf{(D) }10\\qquad\\textbf{(E) }10\\sqrt[3]{10}$\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>The infinite product</p>&#10;<p> <span class=\"katex--display\">\\sqrt[3]{10} \\cdot \\sqrt[3]{\\sqrt[3]{10}} \\cdot \\sqrt[3]{\\sqrt[3]{\\sqrt[3]{10}}} \\cdots</span> <br/>evaluates to a real number. What is that number?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) }\\sqrt{10}\\qquad\\textbf{(B) }\\sqrt[3]{100}\\qquad\\textbf{(C) }\\sqrt[4]{1000}\\qquad\\textbf{(D) }10\\qquad\\textbf{(E) }10\\sqrt[3]{10}</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": 2, "problem_name": "2022 AMC 12A Problem 8", "can_next": true, "can_prev": true, "nxt": "/problem/22_amc12A_p09", "prev": "/problem/22_amc12A_p07"}}