# How do you simplify (z^(1/3))/(z^(-1/2)z^(1/4))?

Jan 11, 2017

See full simplification process below:

#### Explanation:

First, simplify the denominator using the rule for exponents:

${x}^{\textcolor{red}{a}} \times {x}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} + \textcolor{b l u e}{b}}$

$\frac{{z}^{\frac{1}{3}}}{{z}^{\textcolor{red}{- \frac{1}{2}}} {z}^{\textcolor{b l u e}{\frac{1}{4}}}} \to$ z^(1/3)/z^((color(red)(-1/2)+color(blue)(1/4)) $\to$ (z^(1/3))/(z^((color(red)(-2/4)+color(blue)(1/4))  $\to$

${z}^{\frac{1}{3}} / {z}^{- \frac{1}{4}}$

Next, we can simplify the fraction using another rule for exponents:

${x}^{\textcolor{red}{a}} / {x}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} - \textcolor{b l u e}{b}}$

z^color(red)(1/3)/z^color(blue)(-1/4) = z^(color(red)(1/3)-color(blue)(-1/4)) = z^(color(red)(1/3)+color(blue)(1/4)) = z^(color(red)(4/12)+color(blue)(3/12)) = z^(color(red)(7/12)