#### Answer

$\dfrac{5\sqrt[]{ab}}{3}$

#### Work Step by Step

Using the properties of radicals, the given expression, $
\dfrac{\sqrt[]{75ab}}{3\sqrt[]{3}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{1}{3}\sqrt[]{\dfrac{75ab}{3}}
\\\\=
\dfrac{1}{3}\sqrt[]{25ab}
\\\\=
\dfrac{1}{3}\sqrt[]{25\cdot ab}
\\\\=
\dfrac{1}{3}\sqrt[]{(5)^2\cdot ab}
\\\\=
\dfrac{1}{3}\cdot5\sqrt[]{ab}
\\\\=
\dfrac{5\sqrt[]{ab}}{3}
.\end{array}
* Note that it is assumed that all variables represent positive numbers.