We need to simplify the expression:
[tex]\frac{7x^5y-14x^5y^5}{-2x^2y^4}[/tex]We can start by writting:
[tex]\begin{gathered} \frac{7x^5y-14x^5y^5}{-2x^2y^4}=\frac{7x^5y(1-2y^4)^{}}{-2x^2y^4} \\ \\ =-\frac{7}{2}\cdot\frac{x^5}{x^2}\cdot\frac{y}{y^4}\cdot(1-2y^4)^{} \end{gathered}[/tex]Now, we can use the rule:
[tex]\frac{z^a}{z^b}=z^{a-b}[/tex]We obtain:
[tex]\begin{gathered} -\frac{7}{2}x^{5-2}y^{1-4}(1-2y^4) \\ \\ -\frac{7}{2}x^3y^{-3}(1-2y^4) \\ \\ \frac{7}{2}x^3y^{-3}(2y^4-1) \\ \\ \frac{7x^3\mleft(2y^4-1\mright)}{2y^{3}} \end{gathered}[/tex]Therefore, after simplifying, we obtain:
[tex]\frac{7x^3(2y^4-1)}{2y^3}[/tex]