Answer
$-\dfrac{3a^{2}}{2}$
Work Step by Step
Using the laws of exponents, the given expression, $
\dfrac{-15a^{-7}}{10b^{-9}}
$, is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{\cancel{5}\cdot(-3)a^{-7-(-9)}}{\cancel{5}\cdot2}
\\\\=
\dfrac{-3a^{-7+9}}{2}
\\\\=
-\dfrac{3a^{2}}{2}
.\end{array}