Answer
$\dfrac{5\sqrt[5]{4ab^{4}}}{2ab^3}$
Work Step by Step
Rationalizing the denominator of $
\dfrac{5a}{\sqrt[5]{8a^9b^{11}}}
$ results to
\begin{array}{l}
\dfrac{5a}{\sqrt[5]{8a^9b^{11}}}
\cdot
\dfrac{\sqrt[5]{4ab^{4}}}{\sqrt[5]{4ab^{4}}}
\\\\=
\dfrac{5a\sqrt[5]{4ab^{4}}}{\sqrt[5]{32a^{10}b^{15}}}
\\\\=
\dfrac{5a\sqrt[5]{4ab^{4}}}{2a^2b^3}
\\\\=
\dfrac{5\sqrt[5]{4ab^{4}}}{2ab^3}
.\end{array}