Chapter 11.10, Problem 16E

To determine

To find: The exponential form of the given radicals.

Answer to Problem 16E

The exponential form is ${\left(5\right)}^{\frac{5}{7}}$ .

Explanation of Solution

Given:

The given radical is:

  ${\left(\sqrt[7]{5}\right)}^3$

The exponential form is calculated as:

  $\begin{array}{c}{\left(\sqrt[7]{5}\right)}^3={\left(\sqrt[7]{5^1}\right)}^3\\ ={\left({\left(5\right)}^{\frac{1}{7}}\right)}^5\\ ={\left(5\right)}^{\frac{5}{7}}\left[\because {\left(a^m\right)}^n=a^{mn}\right]\end{array}$

Therefore the exponential form is ${\left(5\right)}^{\frac{5}{7}}$ .