Chapter 6.6, Problem 14CYU

To determine

Simplify the expression $\frac{\sqrt[5]{64}}{\sqrt[5]{4}}$ .

Answer to Problem 14CYU

The simplified value of expression $\frac{\sqrt[5]{64}}{\sqrt[5]{4}}$ is $2^{\frac{4}{5}}$ .

Explanation of Solution

Given information: The given expression is $\frac{\sqrt[5]{64}}{\sqrt[5]{4}}$ .

Calculation: The given expression $\frac{\sqrt[5]{64}}{\sqrt[5]{4}}$ can be simplified as,

  $\begin{array}{c}\frac{\sqrt[5]{64}}{\sqrt[5]{4}}=\frac{\sqrt[5]{{\left(2\right)}^6}}{\sqrt[5]{{\left(2\right)}^2}}\\ =\frac{{\left(2\right)}^{\frac{6}{5}}}{{\left(2\right)}^{\frac{2}{5}}}\mathrm{......}\left(\text{Using }\sqrt[n]{x^m}=x^{\frac{m}{n}}\right)\\ ={\left(2\right)}^{\frac{6}{5}-\frac{2}{5}}\mathrm{......}\left(\text{Using }\frac{x^m}{x^n}=x^{m-n}\right)\\ =2^{\frac{4}{5}}\end{array}$