## Elementary Algebra

$4y\sqrt[]{3x}$
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.