Answer
$4a^9-8a^7-\dfrac{5}{12}a^4$
Work Step by Step
Using $a(b+c)=ab+ac$ or the Distributive Property, the given expression, $
\dfrac{2}{3}a^4\left( 6a^5-12a^3-\dfrac{5}{8} \right)
$, is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{2}{3}a^4( 6a^5)+\dfrac{2}{3}a^4(-12a^3)+\dfrac{2}{3}a^4\left(-\dfrac{5}{8} \right)
\\\\=
4a^9-8a^7-\dfrac{10}{24}a^4
\\\\=
4a^9-8a^7-\dfrac{5}{12}a^4
.\end{array}
