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1965 AHSME Problems/Problem 3

Revision as of 15:04, 23 June 2016 by Hiabc (talk | contribs) (Created page with "== Problem == The expression <math>(81)^{-2^{-2}}</math> has the same value as: <math>\textbf{(A)}\ \frac {1}{81} \qquad \textbf{() }\ \frac {1}{3} \qquad \textbf{(C) }\ 3 \...")
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Problem

The expression $(81)^{-2^{-2}}$ has the same value as:

$\textbf{(A)}\ \frac {1}{81} \qquad \textbf{() }\ \frac {1}{3} \qquad \textbf{(C) }\ 3 \qquad \textbf{(D) }\ 81\qquad \textbf{(E) }\ 81^4$

Solution

We know that $81^{-2^{-2}}$ is equivalent to $81^{\frac{1}{-2^2}}=81^{\frac{1}{4}}$, which is the same as $\sqrt[4]{81}=\boxed{3}$.

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