$$(\frac{81y^{16}z^{-8}}{x^{-4}})^{-\frac{1}{4}}$$
$\frac{z^{2}}{3|x|y^{4}}$
$$\frac{\left(81y^{16}z^{-8}\right)^{-\frac{1}{4}}}{\left(x^{-4}\right)^{-\frac{1}{4}}}$$
$$\frac{\left(81y^{16}z^{-8}\right)^{-\frac{1}{4}}}{x^{1}}$$
$$\frac{81^{-\frac{1}{4}}\left(y^{16}\right)^{-\frac{1}{4}}\left(z^{-8}\right)^{-\frac{1}{4}}}{x^{1}}$$
$$\frac{81^{-\frac{1}{4}}y^{-4}\left(z^{-8}\right)^{-\frac{1}{4}}}{x^{1}}$$
$$\frac{81^{-\frac{1}{4}}y^{-4}z^{2}}{x^{1}}$$
$$\frac{\frac{1}{3}y^{-4}z^{2}}{x^{1}}$$
$$\frac{\frac{1}{3}y^{-4}z^{2}}{x}$$
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$-\frac{|x|z^{2}}{3x^{3}y^{4}}$
