Answer
${p=\frac{9{{\pi }^{2}}}{{{N}^{2}}}}$
Work Step by Step
$N=3\pi \sqrt{\frac{1}{p}}$
This is a radical equation.
Use the principle of powers and square both sides of the equation
$\begin{align}
& {{N}^{2}}={{\left( 3\pi \sqrt{\frac{1}{p}} \right)}^{2}} \\
& ={{3}^{2}}\cdot {{\pi }^{2}}\cdot {{\left( \sqrt{\frac{1}{p}} \right)}^{2}} \\
& ={{3}^{2}}\cdot {{\pi }^{2}}\cdot \frac{1}{p}
\end{align}$
Multiply both sides by $p$ to clear fractions
$\begin{align}
& {{N}^{2}}\cdot p={{3}^{2}}\cdot {{\pi }^{2}}\cdot \frac{1}{p}\cdot p \\
& {{N}^{2}}\cdot p={{3}^{2}}\cdot {{\pi }^{2}} \\
\end{align}$
Divide both sides by ${{N}^{2}}$
$\begin{align}
& \frac{{{N}^{2}}p}{{{N}^{2}}}=\frac{9{{\pi }^{2}}}{{{N}^{2}}} \\
& p=\frac{9{{\pi }^{2}}}{{{N}^{2}}}
\end{align}$
