Answer
$x^3y^6$
Work Step by Step
Recall:
(1) $a^{\frac{m}{n}}=\sqrt[n]{a^m}$
(2) $\left(a^m\right)^n=a^{mn}$
(3) $\left(\dfrac{a}{b}\right)^m=\dfrac{a^m}{b^m}$
(4) $a^{-m} = \dfrac{1}{a^m}$
Use rule (3) above to obtain:
\begin{align*}
&=\dfrac{\left(x^{\frac{1}{3}}\right)^9}{\left(y^{-\frac{2}{3}}\right)^9}
\end{align*}
Use rule (2) above to obtain:
\begin{align*}
\dfrac{\left(x^{\frac{1}{3}}\right)^9}{\left(y^{-\frac{2}{3}}\right)^9}&=\dfrac{x^{\frac{1}{3}(9)}}{y^{-\frac{2}{3}(9)}}\\\\
&=\dfrac{x^3}{y^{-6}}
\end{align*}
Use rule (4) above to obtain:
\begin{align*}
&=\dfrac{x^3}{\frac{1}{y^6}}\\\\
&=x^3 \cdot \dfrac{y^6}{1}\\\\
&=x^3y^6
\end{align*}
