The given expression is,
[tex]\frac{-8x^5y^{-2}}{2x^3y^3}[/tex]
Factor out the number:
[tex]\begin{gathered} 8=2\cdot\: 4 \\ =\frac{-2\cdot\:4x^5y^{-2}}{2x^3y^3} \end{gathered}[/tex]
Cancel out the common factor: 2
[tex]=\frac{-4x^5y^{-2}}{x^3y^3}[/tex]
Simplify the above
[tex]\frac{x^5}{x^3}=x^2[/tex]
Therefore,
[tex]=\frac{-4x^2y^{-2}}{y^3}[/tex]
Simplify
[tex]\frac{y^{-2}}{y^3}=\frac{1}{y^5}[/tex][tex]=\frac{-4x^2}{y^5}[/tex]
Apply the fraction rule
[tex]\frac{-a}{b}=-\frac{a}{b}[/tex][tex]=-\frac{4x^2}{y^5}[/tex]
Hence, the answer is
[tex]-\frac{4x^2}{y^5}[/tex]
