Chapter 6.CM, Problem 1CM

To determine

To evaluate:

The given numerical expression.

Answer to Problem 1CM

Solution:

The evaluated value of the given numerical expression is $\frac{8}{27}$.

Explanation of Solution

Given:

The given numerical expression is,

${\left(\frac{3}{2}\right)}^{-3}$

Formula:

The rule for the negative exponents: In order to make the exponents positive, use the reciprocal of the base as,

$b^{-n}=\frac{1}{b^n}$

Calculation:

Use the negative exponent rule,

$\begin{array}{rll}{\left(\frac{3}{2}\right)}^{-3}& =& {\left(\frac{2}{3}\right)}^3\\ & =& \left(\frac{2^3}{3^3}\right)\\ & =& \frac{8}{27}\end{array}$

Conclusion:

Therefore, the evaluated value of the given numerical expression is $\frac{8}{27}$.