Chapter A.2, Problem 8E

To determine

To fill: the blank in given sentence.

Answer to Problem 8E

In the expression $b^{m/n}$ , $m$ denotes the power to which the base is raised and $n$ denotes the index or roots to be taken.

Explanation of Solution

Given information:

In the expression $b^{m/n}$ , $m$ denotes the ------------------to which the base is raised and $n$ denotes the -----------------or root to be taken.

Calculation:

In the expression $b^{m/n}$ ,

  $\begin{array}{c}{b}^{m/n}={\left(b^{1/n}\right)}^m\\ ={\left(\sqrt[n]{b}\right)}^m\\ =\sqrt[n]{b^m}\end{array}$

Here, the numerator $m$ of this rational exponent denotes the power to which the base $b$ , and the denominator $n$ denoted the index or the root to be taken.

Hence,

In the expression $b^{m/n}$ , $m$ denotes the power to which the base is raised and $n$ denotes the index or roots to be taken.