Chapter 7.3, Problem 14P

Simplify each expression.

${(5f)}^{-3}$

To determine

To simplify: The expression ${\left(5f\right)}^{-3}$ .

Answer to Problem 14P

  $\frac{1}{125f^3}$

Explanation of Solution

Given information:

The expression is ${\left(5f\right)}^{-3}$ .

Calculation:

Use multiplication property of exponents which is ${\left(x^a\right)}^b=x^{ab}$ .

  $\begin{array}{c}{\left(5f\right)}^{-3}={\left(5\right)}^{-3}{\left(f\right)}^{-3}\\ =\frac{1}{{\left(5\right)}^3}\cdot \frac{1}{{\left(f\right)}^3}\\ =\frac{1}{125f^3}\end{array}$