Answer
$z^{3/2}$
Work Step by Step
$\begin{array}{ l l }
=\dfrac{z^{3/4} \cdot z^{2}}{z^{5/4}} & \begin{array}{l}
\mathrm{Apply\ the\ rule}\\
\dfrac{1}{a^{-n}} =a^{n}
\end{array}\\
& \\
=\dfrac{z^{\frac{3}{4}+2}}{z^{5/4}} & \begin{array}{l}
\mathrm{Apply\ the\ rule}\\
a^{b} \cdot a^{c} =a^{b+c}
\end{array}\\
& \\
=\dfrac{z^{\frac{3}{4}+\frac{8}{4}}}{z^{5/4}} & \mathrm{Express} \ 2\ \mathrm{as\ } \frac{8}{4}.\\
& \\
=\dfrac{z^{11/4}}{z^{5/4}} & \mathrm{Add\ Exponents.}\\
& \\
=z^{11/4-5/4} & \begin{array}{l}
\mathrm{Apply\ the\ rule}\\
\dfrac{a^{m}}{a^{n}} =a^{m-n}
\end{array}\\
& \\
=z^{6/4} & \mathrm{Subtract\ exponents.}\\
& \\
=z^{3/2} & \mathrm{Simplify\ the\ fraction.}
\end{array}$
