The given expression is
[tex]\frac{4z^7-6z^5}{2z^3}[/tex]First, we factor out the third power of z, and factor 2.
[tex]\frac{2z^3(2z^4-3z^2)}{2z^3}[/tex]Now, we simplify to get the final expression
[tex]2z^4-3z^2[/tex]The divisions made were
[tex]\begin{gathered} \frac{4z^7}{2z^3}=2z^4 \\ \frac{6z^5}{2z^3}=3z^2 \end{gathered}[/tex]