Answer
$\dfrac{ab^3}{\sqrt[]{3ab}}$
Work Step by Step
Rationalizing the numerator, the given expression, $
\sqrt[]{\dfrac{ab^5}{3}}
,$ is equivalent to
\begin{array}{l}
\sqrt[]{\dfrac{ab^5}{3}\cdot\dfrac{ab}{ab}}
\\\\=
\sqrt[]{\dfrac{a^2b^6}{3ab}}
\\\\=
\sqrt[]{\dfrac{(ab^3)^2}{3ab}}
\\\\=
\dfrac{ab^3}{\sqrt[]{3ab}}
.\end{array}