Chapter 7.3, Problem 59PPS

To determine

To find the radical form of the expression ${17}^{\frac{1}{3}}$ .

Answer to Problem 59PPS

  $\sqrt[3]{17}$

Explanation of Solution

Given:

  ${17}^{\frac{1}{3}}$

Formula used:

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

Calculation:$\Rightarrow {17}^{\frac{1}{3}}$

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

The values of m and n are $m=1$ & $n=3$ :

  $\Rightarrow \sqrt[3]{17}$

Conclusion:

Therefore, the radical form of ${17}^{\frac{1}{3}}$ is $\sqrt[3]{17}$ .