The value of $\left[\frac{256 x^{16}}{81 y^{4}}\right]^{-\frac{1}{4}}$ is
(a) $\frac{3 y}{8 x^{4}}$
(b) $\frac{3 y}{4 x^{4}}$
(C) $\frac{4 y}{5 x^{4}}$
(d) $\frac{4 x^{4}}{3 y}$
$\left[\frac{256 x^{16}}{81 y^{4}}\right]^{-\frac{1}{4}}=\left[\frac{2^{8} x^{16}}{3^{4} y^{4}}\right]^{-\frac{1}{4}}$
$=\left[\frac{3^{4} y^{4}}{2^{8} x^{16}}\right]^{\frac{1}{4}}$
$=\left[\frac{\left(3^{4}\right)^{\frac{1}{4}}\left(y^{4}\right)^{\frac{1}{4}}}{\left(2^{8}\right)^{\frac{1}{4}}\left(x^{16}\right)^{\frac{1}{4}}}\right]$
$=\left[\frac{3 y}{2^{2} x^{4}}\right]$
$=\frac{3 y}{4 x^{4}}$
$\therefore$ The value of $\left[\frac{256 x^{16}}{81 y^{4}}\right]^{-\frac{1}{4}}$ is $\frac{3 y}{4 x^{4}}$.
Hence, the correct option is (b).
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