Answer
$\dfrac{16}{375}$
Work Step by Step
Using the laws of exponents, the given expression $
\dfrac{\left( \dfrac{1}{2} \right)^3\left( \dfrac{2}{3} \right)^4}{\left( \dfrac{5}{6} \right)^3}
$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{1}{8}\cdot\dfrac{16}{81}\div\dfrac{125}{216}
\\\\=
\dfrac{1}{8}\cdot\dfrac{16}{81}\cdot\dfrac{216}{125}
\\\\=
\dfrac{1}{\cancel{8}}\cdot\dfrac{\cancel{8}\cdot2}{\cancel{27}\cdot3}\cdot\dfrac{\cancel{27}\cdot8}{125}
\\\\=
\dfrac{16}{375}
.\end{array}
