Chapter 11.10, Problem 14E

To determine

To find: The exponential form of the given radicals.

Answer to Problem 14E

The exponential form is ${\left(7\right)}^{\frac{5}{2}}$ .

Explanation of Solution

Given:

The given radical is:

  ${\left(\sqrt{7}\right)}^5$

The exponential form is calculated as:

  $\begin{array}{c}{\left(\sqrt{7}\right)}^5={\left(\sqrt[2]{7^1}\right)}^5\\ ={\left({\left(7\right)}^{\frac{1}{2}}\right)}^5\\ ={\left(7\right)}^{\frac{5}{2}}\left[\because {\left(a^m\right)}^n=a^{mn}\right]\end{array}$

Therefore the exponential form is ${\left(7\right)}^{\frac{5}{2}}$ .