Answer
$4y\sqrt[]{3x}$
Work Step by Step
Using the properties of radicals, the given expression, $
\dfrac{4}{3}\sqrt[]{27xy^2}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{4}{3}\sqrt[]{9y^2\cdot3x}
\\\\=
\dfrac{4}{3}\sqrt[]{(3y)^2\cdot3x}
\\\\=
\dfrac{4}{3}\cdot3y\sqrt[]{3x}
\\\\=
\dfrac{4}{\cancel{3}}\cdot\cancel{3}y\sqrt[]{3x}
\\\\=
4y\sqrt[]{3x}
.\end{array}
Note that all variables are assumed to have positive values.
