Answer
$\dfrac{\sqrt[3]{5a^2b}}{ab}$
Work Step by Step
Rationalizing the denominator of the given expression, $
\sqrt[3]{\dfrac{5}{ab^2}}
,$ we find:
\begin{array}{l}\require{cancel}
\sqrt[3]{\dfrac{5}{ab^2}\cdot\dfrac{a^2b}{a^2b}}
\\\\=
\sqrt[3]{\dfrac{5a^2b}{a^3b^3}}
\\\\=
\dfrac{\sqrt[3]{5a^2b}}{\sqrt[3]{a^3b^3}}
\\\\=
\dfrac{\sqrt[3]{5a^2b}}{\sqrt[3]{(ab)^3}}
\\\\=
\dfrac{\sqrt[3]{5a^2b}}{ab}
.\end{array}
* Note that it is assumed that all variables represent positive numbers.