Answer
$p^2$
Work Step by Step
$\begin{array}{|l|c|}
\hline
=\dfrac{p^{( 1/5+7/10+1/2)}}{\left( p^{3}\right)^{-1/5}} & \begin{array}{l}
\mathrm{Apply\ the\ rule}\\
a^{m} \cdot a^{n} =a^{m+n}
\end{array}\\
& \\
\hline
=\dfrac{p^{( 2/10+7/10+5/10)}}{\left( p^{3}\right)^{-1/5}} & \begin{array}{l}
\mathrm{The\ LCD\ of\ the\ fractional}\\
\mathrm{exponents\ is} \ \mathrm{ten} .\\
\dfrac{1}{5} =\dfrac{2}{10} \ \mathrm{and} \ \dfrac{1}{2} =\dfrac{5}{10}
\end{array}\\
& \\
\hline
=\dfrac{p^{( 14/10)}}{\left( p^{3}\right)^{-1/5}} & \mathrm{Combine\ fractions.}\\
& \\
\hline
=p^{7/5}\left( p^{3}\right)^{1/5} & \begin{array}{l}
\mathrm{Reduce} \ \dfrac{14}{10} \ \mathrm{to} \ \dfrac{7}{5}.\\
\\
\mathrm{Apply\ the\ rule}\\
\dfrac{1}{a^{-n}} =a^{n}
\end{array}\\
& \\
\hline
=p^{7/5} \cdot p^{3/5} & \begin{array}{l}
\mathrm{Apply\ the\ rule}\\
\left( a^{m}\right)^{n} =a^{m\cdot n}
\end{array}\\
& \\
\hline
=p^{7/5+3/5} & \begin{array}{l}
\mathrm{Apply\ the\ rule}\\
a^{m} \cdot a^{n} =a^{m+n}
\end{array}\\
& \\
\hline
=p^{10/5} & \mathrm{Add\ fractional\ exponents}\\
& \\
\hline
=p^{2} & \mathrm{Simplify}\\
\hline
\end{array}$
