The value of

$\sqrt[4]{(64)^{-2}}=\left[(64)^{-2}\right]^{\frac{1}{4}}$

$=\left[\left(2^{6}\right)^{-2}\right]^{\frac{1}{4}}$

$=\left[2^{-12}\right]^{\frac{1}{4}}$

$=2^{-3}$

$=\frac{1}{2^{3}}$

$=\frac{1}{8}$

$\therefore$ The value of $\sqrt[4]{(64)^{-2}}$ is $\frac{1}{8}$.

Hence, the correct option is (a).