Answer
$\dfrac{3x\sqrt[3]{3}}{2}$
Work Step by Step
Using the properties of radicals, the given expression, $
\dfrac{3}{4}\sqrt[3]{24x^3}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{3}{4}\sqrt[3]{8x^3\cdot3}
\\\\=
\dfrac{3}{4}\sqrt[3]{(2x)^3\cdot3}
\\\\=
\dfrac{3}{4}\cdot2x\sqrt[3]{3}
\\\\=
\dfrac{3}{\cancel{2}(2)}\cdot\cancel{2}x\sqrt[3]{3}
\\\\=
\dfrac{3x\sqrt[3]{3}}{2}
.\end{array}
Note that all variables are assumed to have positive values.
