Answer
$\dfrac{10}{3}$
Work Step by Step
Using the properties of radicals, the given expression, $
\sqrt[3]{\dfrac{1000}{27}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt[3]{1000}}{\sqrt[3]{27}}
\\\\=
\dfrac{\sqrt[3]{(10)^3}}{\sqrt[3]{(3)^3}}
\\\\=
\dfrac{10}{3}
\end{array}