Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 1.8 Junior Find the answer

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

Pick one

Solution

Let us recall $\text{PEMDAS}$ . We 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

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.