Answer
$-\frac{3}{x}$
Work Step by Step
The quotient rule for radicals tells us that $\sqrt[n] \frac{a}{b}=\frac{\sqrt[n] a}{\sqrt[n] b}$ (if $\sqrt[n] a$ and $\sqrt[n] b$ are real numbers and $n$ is a natural number). That is, the nth root of a quotient is the quotient of the nth roots.
Therefore, $-\sqrt[4] \frac{81}{x^{4}}=-\frac{\sqrt[4] 81}{\sqrt[4] x^{4}}=-\frac{3}{x}$.
$\sqrt[4] 81=3$, because $3^{4}=81$
$\sqrt[4] x^{4}=x$, because $(x)^{4}=x^{4}$
