#### Answer

$\dfrac{8}{3}\sqrt{5xy}$

#### Work Step by Step

Using the properties of radicals, the given expression, $
\dfrac{4}{3}\sqrt{20xy}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{4}{3}\sqrt{4\cdot5xy}
\\\\=
\dfrac{4}{3}\sqrt{(2)^2\cdot5xy}
\\\\=
\dfrac{4}{3}\cdot2\sqrt{5xy}
\\\\=
\dfrac{8}{3}\sqrt{5xy}
.\end{array}
Note that all of the variables are assumed to represent non-negative real numbers.