Answer
$-\dfrac{4\sqrt[3]{x^2}}{3}$
Work Step by Step
Using the properties of radicals, the given expression, $
\dfrac{\sqrt[3]{128x^3}}{-3\sqrt[3]{2x}}
,$ simplifies to
\begin{array}{l}\require{cancel}
-\dfrac{1}{3}\sqrt[3]{\dfrac{128x^3}{2x}}
\\\\=
-\dfrac{1}{3}\sqrt[3]{64x^2}
\\\\=
-\dfrac{1}{3}\sqrt[3]{64\cdot x^2}
\\\\=
-\dfrac{1}{3}\sqrt[3]{(4)^3\cdot x^2}
\\\\=
-\dfrac{1}{3}\cdot4\sqrt[3]{x^2}
\\\\=
-\dfrac{4\sqrt[3]{x^2}}{3}
.\end{array}
