Chapter 7.3, Problem 60PPS

To determine

To find the radical form of the expression $q^{\frac{1}{4}}$ .

Answer to Problem 60PPS

  $\sqrt[4]{q}$

Explanation of Solution

Given:

  $q^{\frac{1}{4}}$

Formula used:

  $x^{\frac{m}{n}}={(x^{\frac{1}{n}})}^m={(\sqrt[n]{x})}^m$

Calculation:$\Rightarrow q^{\frac{1}{4}}$

Using above formula, $x^{\frac{m}{n}}={(x^{\frac{1}{n}})}^m={(\sqrt[n]{x})}^m$

The values of m and n are $m=1$ & $n=4$ :

  $\Rightarrow \sqrt[4]{q}$

Conclusion:

Therefore, the radical form of $q^{\frac{1}{4}}$ is $\sqrt[4]{q}$ .