Answer
$-\dfrac{\sqrt[3]{50p}}{5p}$
Work Step by Step
The given expression, $
-\sqrt[3]{\dfrac{2}{5p^2}}
,$ simplifies to
\begin{array}{l}\require{cancel}
-\sqrt[3]{\dfrac{2}{5p^2}\cdot\dfrac{5^2p}{5^2p}}
\\\\=
-\sqrt[3]{\dfrac{2(25p)}{5^3p^3}}
\\\\=
-\sqrt[3]{\dfrac{50p}{(5p)^3}}
\\\\=
-\dfrac{\sqrt[3]{50p}}{\sqrt[3]{(5p)^3}}
\\\\=
-\dfrac{\sqrt[3]{50p}}{5p}
.\end{array}
