Answer
The simplest form of the expression ${{\left( -2{{x}^{2}}{{y}^{-3}} \right)}^{-4}}$ is $\frac{{{y}^{12}}}{16{{x}^{8}}}$.
Work Step by Step
Consider the expression.
${{\left( -2{{x}^{2}}{{y}^{-3}} \right)}^{-4}}$
Apply the power rule as follows.
$\begin{align}
& {{\left( -2{{x}^{2}}{{y}^{-3}} \right)}^{-4}}={{\left( -2 \right)}^{-4}}{{\left( {{x}^{2}} \right)}^{-4}}{{\left( {{y}^{-3}} \right)}^{-4}} \\
& ={{\left( -2 \right)}^{-4}}\left( {{x}^{-8}} \right)\left( {{y}^{12}} \right)
\end{align}$
Apply the negative exponent rule,
$\begin{align}
& {{\left( -2{{x}^{2}}{{y}^{-3}} \right)}^{-4}}=\frac{{{y}^{12}}}{{{\left( -2 \right)}^{4}}{{x}^{8}}} \\
& =\frac{{{y}^{12}}}{16{{x}^{8}}}
\end{align}$
