Answer
$3xy$
Work Step by Step
Recall:
If $\sqrt[n]{a}$ and $\sqrt[n]{b}$ are real numbers, then $\dfrac{\sqrt[n]{a}}{\sqrt[n]{b}}=\sqrt[n]{\dfrac{a}{b}},$ where $a\ne0$.
Use the rule above to obtain:
\begin{align*}
\require{cancel}
\dfrac{\sqrt[3]{81x^5y^3}}{\sqrt[3]{3x^2}}&=\sqrt[3]{\dfrac{81x^5y^3}{3x^2}}\\\\
&=\sqrt[3]{\dfrac{\cancel{81}^{27}x^{\cancel{5}3}y^3}{\cancel{3}\cancel{x^2}}}\\\\
&=\sqrt[3]{27x^3y^3}\\\\
&=\sqrt[3]{3xy)(3xy)(3xy)}\\\\
&=\sqrt[3]{\left(3xy\right)^3}
\end{align*}
Use the rule $\sqrt[n]{a^n} = a$ where $a$ is odd to obtain:
$$=3xy$$
