Chapter 7.3, Problem 27P

Simplify each expression.

${\left(3b^{-4}{c}^{-2}\right)}^6{c}^3$

To determine

To simplify: The provided expression.

Answer to Problem 27P

The simplified expression $\frac{729}{b^{24}{c}^9}$ .

Explanation of Solution

Given:

The expression is:

  ${\left(3b^{-4}{c}^{-2}\right)}^6{c}^3$

Calculation:

The provided expression could be simplified as:

  $\begin{array}{c}{\left(3b^{-4}{c}^{-2}\right)}^6{c}^3=\left(3^6{b}^{-6\times 4}{c}^{-2\times 6}\right)c^3\\ =\left(729b^{-24}{c}^{-12}\right)c^3\\ =\frac{729c^{-12+3}}{b^{24}}\\ =\frac{729}{b^{24}{c}^9}\end{array}$

Thus, the simplified expression is $\frac{729}{b^{24}{c}^9}$ .