Question:
The value of $\sqrt[4]{(64)^{-2}}$ is
(a) $\frac{1}{8}$
(b) $\frac{1}{2}$
(c) 8
(d) $\frac{1}{64}$
Solution:
$\sqrt[4]{(64)^{-2}}=\left[(64)^{-2}\right]^{\frac{1}{4}}$
$=\left[\left(2^{6}\right)^{-2}\right]^{\frac{1}{4}}$
$=\left[2^{-12}\right]^{\frac{1}{4}}$
$=2^{-3}$
$=\frac{1}{2^{3}}$
$=\frac{1}{8}$
$\therefore$ The value of $\sqrt[4]{(64)^{-2}}$ is $\frac{1}{8}$.
Hence, the correct option is (a).
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