What is (z/(z^{1/3)})^{1/2} ?

The solution to (z/(z^{1/3)})^{1/2} is z^{1/3}

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simplify (z/(z^{1/3)})^{1/2}

simplify

(\frac{z}{z ^{\frac{1}{3}}})^{\frac{1}{2}}

z^{\frac{1}{3}}

Solution steps

(\frac{z}{z ^{\frac{1}{3}}})^{\frac{1}{2}}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{z ^{\frac{1}{2}}}{( z ^{\frac{1}{3}} ) ^{\frac{1}{2}}}

Simplify

(z^{\frac{1}{3}})^{\frac{1}{2}} : z^{\frac{1}{6}}

= \frac{z ^{\frac{1}{2}}}{z ^{\frac{1}{6}}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{z ^{\frac{1}{2}}}{z ^{\frac{1}{6}}} = z^{\frac{1}{2} - \frac{1}{6}}

= z^{\frac{1}{2} - \frac{1}{6}}

Subtract the numbers:

\frac{1}{2} - \frac{1}{6} = \frac{1}{3}

= z^{\frac{1}{3}}

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