Chapter 5.1, Problem 31E

To determine

To evaluate : the given expression using a calculator.

Answer to Problem 31E

The solution of the given expression is $\underset{\_}{50.57}$ .

Explanation of Solution

Given information :

The given expression:

  ${\left(\sqrt[4]{187}\right)}^3$

Concept used :

Let $a^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$n$}\right.}$ be an $n\text{th}$ root of $a$ and let $m$ be a positive integer.

  $a^{\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$n$}\right.}={\left(a^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$n$}\right.}\right)}^m={\left(\sqrt[n]{a}\right)}^m$

Calculation :

As per problem,

The given expression:

  ${\left(\sqrt[4]{187}\right)}^3$

Before evaluating the given expression, rewrite the expression in rational exponential form

  $\begin{array}{l}{\left(\sqrt[4]{187}\right)}^3={\text{ 187}}^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}\text{ [Write in rational exponential form }{a}^{\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$n$}\right.}\text{]}\\ \approx 50.57\text{ [Use a calculalator]}\end{array}$

The solution of the given expression is $50.57$ .