Chapter 6.6, Problem 56PPS

To determine

Simplify the expression $\frac{z^{\frac{4}{5}}}{z^{\frac{1}{2}}}$ .

Answer to Problem 56PPS

The simplified value of expression $\frac{z^{\frac{4}{5}}}{z^{\frac{1}{2}}}$ is $z^{\frac{3}{10}}$ .

Explanation of Solution

Given information: The given expression is $\frac{z^{\frac{4}{5}}}{z^{\frac{1}{2}}}$ .

Calculation: The given expression $\frac{z^{\frac{4}{5}}}{z^{\frac{1}{2}}}$ can be simplified as,

  $\begin{array}{c}\frac{z^{\frac{4}{5}}}{z^{\frac{1}{2}}}={\left(z\right)}^{\frac{4}{5}-\frac{1}{2}}\mathrm{......}\left(\text{Using }\frac{{\left(x\right)}^m}{{\left(x\right)}^n}={\left(x\right)}^{m-n}\right)\\ ={\left(z\right)}^{\frac{8-5}{10}}\\ =z^{\frac{3}{10}}\end{array}$