Answer
$-\dfrac{27x^{10}}{y^2}$
Work Step by Step
Using $x^m\cdot x^n=x^{m+n}$ the given expression, $
\left(-9x^2y^5\right)\left(3x^8y^{-7}\right)
,$ is equivalent to
\begin{align*}
&
(-9\cdot3)x^{2+8}y^{5+(-7)}
\\&=
-27x^{10}y^{-2}
.\end{align*}
Using $x^{-m}=\dfrac{1}{x^m}$ the expression above is equivalent to
\begin{align*}
&
-\dfrac{27x^{10}}{y^2}
.\end{align*}
Hence, the expression $\left(-9x^2y^5\right)\left(3x^8y^{-7}\right)$ simplifies to $-\dfrac{27x^{10}}{y^2}$.
