{"status": "success", "data": {"description_md": "According to the standard convention for exponentiation, \n\n$$2^{2^{2^{2}}} = 2^{\\left(2^{\\left(2^2\\right)}\\right)} = 2^{16} = 65536.$$<br>If the order in which the exponentiations are performed is changed, how many other values are possible?\n\n$\\mathrm{(A) \\ } 0\\qquad \\mathrm{(B) \\ } 1\\qquad \\mathrm{(C) \\ } 2\\qquad \\mathrm{(D) \\ } 3\\qquad \\mathrm{(E) \\ } 4$\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>According to the standard convention for exponentiation,</p>&#10;<p> <span class=\"katex--display\">2^{2^{2^{2}}} = 2^{\\left(2^{\\left(2^2\\right)}\\right)} = 2^{16} = 65536.</span> <br/>If the order in which the exponentiations are performed is changed, how many other values are possible?</p>&#10;<p> <span class=\"katex--inline\">\\mathrm{(A) \\ } 0\\qquad \\mathrm{(B) \\ } 1\\qquad \\mathrm{(C) \\ } 2\\qquad \\mathrm{(D) \\ } 3\\qquad \\mathrm{(E) \\ } 4</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": "2002 AMC 12A Problem 3", "can_next": true, "can_prev": true, "nxt": "/problem/02_amc12A_p04", "prev": "/problem/02_amc12A_p02"}}