Chapter 11.10, Problem 12E

To determine

To find: The exponential form of the given radicals.

Answer to Problem 12E

The exponential form is ${\left(8\right)}^{\frac{5}{6}}$ .

Explanation of Solution

Given:

The given radical is:

  ${\left(\sqrt[6]{8}\right)}^5$

The exponential form is calculated as:

  $\begin{array}{c}{\left(\sqrt[6]{8}\right)}^5={\left(\sqrt[6]{{\left(8\right)}^1}\right)}^5\\ ={\left({\left(8\right)}^{\frac{1}{6}}\right)}^5\\ =8^{\frac{5}{6}}\left[\because {\left(a^m\right)}^n=a^{mn}\right]\end{array}$

Therefore the exponential form is ${\left(8\right)}^{\frac{5}{6}}$ .