Answer:
[tex]z^{\frac{5}{6}}[/tex]
Step-by-step explanation:
[tex]\frac{z^{\frac{1}{3}}}{z^{-\frac{3}{4}}z^{\frac{1}{4}}}[/tex]
[tex]z^{-\frac{3}{4}}z^{\frac{1}{4}}[/tex]
[tex]=z^{-\frac{3}{4}+\frac{1}{4}}[/tex]
[tex]=\frac{z^{\frac{1}{3}}}{z^{-\frac{3}{4}+\frac{1}{4}}}[/tex]
[tex]=z^{\frac{1}{3}-\left(\frac{1}{4}-\frac{3}{4}\right)}[/tex]
[tex]=z^{\frac{5}{6}}[/tex]
