Answer
$11.86 $ years
Work Step by Step
Given \begin{equation}
a=\sqrt[3]{P^2}= P^{\frac{2}{3}}.
\end{equation} First solve for $P$ in terms of $a$. \begin{equation}
\begin{aligned}
P^{\frac{2}{3}}&=a\\
\left(P^{\frac{2}{3}} \right)^{\frac{3}{2}}& =\left( a\right)^{\frac{3}{2}}\\
P& = a^{\frac{3}{2}}.
\end{aligned}
\end{equation} Now, set $a= 5.2$ to find the number of years that it takes Pluto to orbit the sun.
\begin{equation}
\begin{aligned}
P& = 5.2^{\frac{3}{2}}\\
&=11.86.
\end{aligned}
\end{equation} It will take Jupiter about $11.86 $ years to orbit the sun.
