Answer
$\color{blue}{z^{3/2}}$
Work Step by Step
RECALL:
(1) $a^m \cdot a^n = a^{m+n}$
(2) $\dfrac{a^m}{a^n} = a^{m-n}$
(3) $a^{1/n} = \sqrt[n]{a}$
(4) When $n$ is odd, $\sqrt[n]{a^n}=a$
(5) $a^{m/n} = \left(\sqrt[n]{a}\right)^m$
Use rule (1) above to obtain:
$=\dfrac{z^{3/4}}{z^{5/4+(-2)}}
\\=\dfrac{z^{3/4}}{z^{5/4+(-8/4)}}
\\=\dfrac{z^{3/4}}{z^{-3/4}}$
Use rule (2) above to obtain:
$=z^{3/4 - (-3/4)}
\\=z^{3/4+3/4}
\\=z^{6/4}
\\=\color{blue}{z^{3/2}}$
