Answer
$a^{7/12}-a^{7/3}$
Work Step by Step
The given expression, $
a^{-2/3}\left( a^{5/4}-a^3 \right)
,$ simplifies to
\begin{array}{l}\require{cancel}
a^{\frac{-2}{3}}\cdot a^{\frac{5}{4}}+a^{\frac{-2}{3}}\cdot\left( -a^3 \right)
\\\\=
a^{\frac{-2}{3}+\frac{5}{4}}-a^{\frac{-2}{3}+3}
\\\\=
a^{\frac{-8}{12}+\frac{15}{12}}-a^{\frac{-2}{3}+\frac{9}{3}}
\\\\=
a^{\frac{7}{12}}-a^{\frac{7}{3}}
\\\\=
a^{7/12}-a^{7/3}
.\end{array}
