Answer
$\dfrac{10}{a^{1/8}\cdot b^{3/2}}$
Work Step by Step
$\begin{array}{ l c }
=\left(\dfrac{25^{4/8} \cdot a^{3/8}}{b^{2/8}}\right)\left(\dfrac{4^{2/4} \cdot b^{-5/4}}{a^{2/4}}\right) & \begin{array}{l}
\mathrm{Apply\ the\ rule}\\
\left(\dfrac{a^{b}}{b^{d}}\right)^{n} =\dfrac{a^{bn}}{b^{dn}}
\end{array}\\
& \\
=\left(\dfrac{25^{1/2} \cdot a^{3/8}}{b^{1/4}}\right)\left(\dfrac{4^{1/2}\cdot b^{-5/4}}{a^{1/2} }\right) & \mathrm{Reduce\ the\ fraction\ in\ the\ exponent}\\
& \\
=\left(\dfrac{25^{1/2} \cdot a^{3/8}}{b^{1/4}}\right)\left(\dfrac{4^{1/2}}{a^{1/2} \cdot b^{5/4}}\right) & \text{Use the rule }a^{-n}=\dfrac{1}{a^n}.\\\
& \\
=\left(\dfrac{\sqrt{25} \cdot a^{3/8}}{b^{1/4}}\right)\left(\dfrac{\sqrt{4}}{a^{1/2} \cdot b^{5/4}}\right) & \begin{array}{l}
\mathrm{For\ numerical\ expressions,\ }\\
\mathrm{apply\ the\ rule} \ a^{1/n} =\sqrt{a}.
\end{array}\\
& \\
=\left(\dfrac{5\cdot a^{3/8}}{b^{1/4}}\right)\left(\dfrac{2}{a^{1/2} \cdot b^{5/4}}\right) & \mathrm{Simplify\ the\ numerical\ expressions.}\\
& \\
=\dfrac{10a^{3/8}}{a^{1/2}\cdot b^{1/4} \cdot b^{5/4}} & \begin{array}{l}
\mathrm{Multiply\ the\ rational\ expressions}\\
\left(\dfrac{a}{b}\right)\left(\dfrac{c}{d}\right) =\dfrac{ac}{bd}
\end{array}\\
& \\
=\dfrac{10a^{3/8}}{a^{4/8}\left(b^{1/4+5/4}\right)} & \begin{array}{l}
\mathrm{Rewrite} \ 1/2\ \mathrm{as} \ 4/8\mathrm{\ }\\
\mathrm{apply\ the\ rule} \ a^{b} \cdot a^{c} =a^{b+c}
\end{array}\\
& \\
=\dfrac{10}{\left(a^{4/8-3/8}\right)\left(b^{1/4+5/4}\right)} & \begin{array}{l}
\mathrm{Apply\ the\ rule}\\
\dfrac{a^{b}}{a^{c}} =\dfrac{1}{a^{c-b}}
\end{array}\\
& \\
=\dfrac{10}{a^{1/8} \cdot b^{6/4}} & \mathrm{Simplify.}\\
& \\
=\dfrac{10}{a^{1/8} \cdot b^{3/2}} &
\end{array}$
