Chapter 11.3, Problem 47E

To determine

The simplified form of expression.

Answer to Problem 47E

  $\frac{1}{{18}^{\frac{2}{3}}}$

Explanation of Solution

Given:

The given expression is ${\left(6^{\frac{1}{3}}\cdot 3^{\frac{1}{3}}\right)}^{-2}$

Calculation:

Consider the expression-

  $\begin{array}{l}{\left(6^{\frac{1}{3}}\cdot 3^{\frac{1}{3}}\right)}^{-2}\\ ={\left({18}^{\frac{1}{3}}\right)}^{-2}\{{\left({\mathrm{a}}^{\mathrm{m}}\right)}^{\mathrm{n}}={\mathrm{a}}^{\mathrm{m}\mathrm{n}}\}\\ ={18}^{-\frac{2}{3}}\\ =\frac{1}{{18}^{\frac{2}{3}}}\end{array}$