Answer
$$\nabla h =\left\langle y z^{-3}, x z^{-3},-3 x y z^{-4}\right\rangle$$
Work Step by Step
Given
$$ h(x, y, z)=x y z^{-3}$$
Since
\begin{align*}
\frac{\partial h}{\partial x}&=y z^{-3}\\
\frac{\partial h}{\partial y}&=x z^{-3}\\
\frac{\partial h}{\partial z}&= -3 x y z^{-4}
\end{align*}
Then
\begin{align*}
\nabla h&=\left\langle\frac{\partial h}{\partial x}, \frac{\partial h}{\partial y}, \frac{\partial h}{\partial z}\right\rangle\\
&=\left\langle y z^{-3}, x z^{-3},-3 x y z^{-4}\right\rangle
\end{align*}
