1965 AHSME Problems/Problem 3

Problem

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

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

Solution

Let us recall $PEMDAS$ . We realize that we have to calculate the exponent first. $(-2)^{-2}=\frac{1}{(-2)^2}=\frac{1}{4}$ When we substitute, we get $81^\frac{1}{4}=\sqrt[4]{81}=\boxed{\textbf{(C) }3}$ .

~Mathfun1000 (Explaining clearly)

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1965 AHSME Problems/Problem 3

Problem

Solution