https://artofproblemsolving.com/wiki/index.php?title=1972_AHSME_Problems/Problem_5&feed=atom&action=history 1972 AHSME Problems/Problem 5 - Revision history 2021-11-30T04:14:54Z Revision history for this page on the wiki MediaWiki 1.31.1 https://artofproblemsolving.com/wiki/index.php?title=1972_AHSME_Problems/Problem_5&diff=136869&oldid=prev Lopkiloinm: Created page with "== Problem 5 == From among $2^{1/2}, 3^{1/3}, 8^{1/8}, 9^{1/9}$ those which have the greatest and the next to the greatest values, in that order, are [itex]\tex..." 2020-11-07T06:01:09Z <p>Created page with &quot;== Problem 5 == From among &lt;math&gt;2^{1/2}, 3^{1/3}, 8^{1/8}, 9^{1/9}&lt;/math&gt; those which have the greatest and the next to the greatest values, in that order, are &lt;math&gt;\tex...&quot;</p> <p><b>New page</b></p><div>== Problem 5 ==<br /> <br /> From among &lt;math&gt;2^{1/2}, 3^{1/3}, 8^{1/8}, 9^{1/9}&lt;/math&gt; those which have the greatest and the next to the greatest values, in that order, are <br /> <br /> &lt;math&gt;\textbf{(A) } 3^{1/3},\ 2^{1/2}\quad <br /> \textbf{(B) } 3^{1/3},\ 8^{1/8}\quad <br /> \textbf{(C) } 3^{1/3},\ 9^{1/9}\quad <br /> \textbf{(D) } 8^{1/8},\ 9^{1/9}\quad \\ <br /> \text{(E) None of these}&lt;/math&gt;<br /> <br /> == Solution ==<br /> <br /> &lt;math&gt;8^{1/8}&lt;/math&gt; and &lt;math&gt;9^{1/9}&lt;/math&gt; are obviously too small. We must then compare &lt;math&gt;3^{1/3}&lt;/math&gt; with &lt;math&gt;2^{1/2}&lt;/math&gt;. Raising both to the power of &lt;math&gt;6&lt;/math&gt; gives &lt;math&gt;9&lt;/math&gt; and &lt;math&gt;8&lt;/math&gt; respectively. Our answer is therefore &lt;math&gt;\boxed{\textbf{(A) } 3^{1/3},\ 2^{1/2}}.&lt;/math&gt; ~lopkiloinm</div> Lopkiloinm