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The value of

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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