Answer
$-\dfrac{4}{15}$
Work Step by Step
Using order of operations, the expression $
\left( -\dfrac{2}{3} \right)^3\div\dfrac{10}{9}
$ simplifies to
\begin{array}{l}
-\dfrac{8}{27}\cdot\dfrac{9}{10}
\\\\=
-\dfrac{2\cdot4}{9\cdot3}\cdot\dfrac{9}{2\cdot5}
\\\\=
-\dfrac{4}{3}\cdot\dfrac{1}{5}
\\\\=
-\dfrac{4}{15}
.\end{array}
