Answer:
[tex]z^{ \frac{1}{3}[/tex]
Step-by-step explanation:
[tex]\sqrt{\frac{z}{z^{\frac{1}{3}} } } = \sqrt{z \times z^{-\frac{1}{3}}[/tex] [tex][ \ \frac{a}{a^x} = a \cdot a^{-x} \ ][/tex]
[tex]= \sqrt {z^{\frac{2}{3}}}\\\\[/tex] [tex][ \ a^x \cdot a^y = a^{ x+ y} \ ][/tex]
[tex]= (z^{\frac{2}{3}})^{ \frac{1}{2}}[/tex] [tex][ \ \sqrt{x^y} = (x^{y}) ^{\frac{1}{2}} \ ][/tex]
[tex]= z^ {\frac{1}{3}}[/tex] [tex][ \ (a^x)^y = a^{xy} \ ][/tex]
