Answer
Perimeter: $2x^{2/3}(x^{7/3}+2)$
Area: $2x^{11/3}$
Work Step by Step
We find the perimeter of the rectangle:
$$\begin{align*}
\text{Perimeter}&=2\cdot\text{Length}+2\cdot\text{Width}\\
&=2x^3+2(2x^{2/3})\\
&=2x^3+4x^{2/3}\\
&=2x^{2/3}(x^{7/3}+2).
\end{align*}$$
We find the area of the rectangle:
$$\begin{align*}
\text{Area}&=\text{Length}\cdot\text{Width}\\
&=x^3\cdot 2x^{2/3}\\
&=2x^{3+(2/3)}\\
&=2x^{11/3}.
\end{align*}$$
