Answer
The simplest form of the expression $\left( -5{{x}^{4}}{{y}^{-3}}{{z}^{2}} \right)\left( -4{{x}^{2}}{{y}^{2}} \right)$ is $\frac{20{{x}^{6}}{{z}^{2}}}{y}$.
Work Step by Step
Consider the expression.
$\left( -5{{x}^{4}}{{y}^{-3}}{{z}^{2}} \right)\left( -4{{x}^{2}}{{y}^{2}} \right)$
Apply product rule as follows.
$\begin{align}
& \left( -5{{x}^{4}}{{y}^{-3}}{{z}^{2}} \right)\left( -4{{x}^{2}}{{y}^{2}} \right)=20{{x}^{4+2}}{{y}^{-3+2}}{{z}^{2}} \\
& =20{{x}^{6}}{{y}^{-1}}{{z}^{2}}
\end{align}$
Apply the negative exponent rule:
$\left( -5{{x}^{4}}{{y}^{-3}}{{z}^{2}} \right)\left( -4{{x}^{2}}{{y}^{2}} \right)=\frac{20{{x}^{6}}{{z}^{2}}}{y}$
