Chapter 5.1, Problem 1E

To determine

To write: The given expression in radical form stating the index of the radical.

Answer to Problem 1E

The given expression in radical form is:

  $\frac{1}{{\left(\sqrt[t]{a}\right)}^s}$

The index of the radical is $t$ .

Explanation of Solution

Given information:

The following expression:

  $a^{-s/t}$

Calculation:

The following expression can be written in the radical form as follows:

  $\begin{array}{l}{a}^{-s/t}\text{[Given]}\\ $ ={(a^{-1/t})}^s[\text{Power of a power property]}$={\left(\frac{1}{a^{1/t}}\right)}^s[\text{Negative exponent rule]}\\ =\frac{1}{{\left(\sqrt[t]{a}\right)}^s}[\text{Representing in radical form]}\end{array}$

The index of the radical is $t$ .