Answer
$\frac{p^{3}}{9}$
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, $\sqrt \frac{p^{6}}{81}=\frac{\sqrt p^{6}}{\sqrt 81}=\frac{p^{3}}{9}$.
$\sqrt p^{6}=p^{3}$, because $(p^{3})^{2}=p^{3\times2}=p^{6}$
$\sqrt 81=9$, because $9^{2}=81$
