Chapter 7.9, Problem 10OE

To determine

To calculate: The simplified form of the expression $4^{-3}$ .

Answer to Problem 10OE

The simplified form of the expression $4^{-3}$ is $\frac{1}{64}$ .

Explanation of Solution

Given information:

The expression $4^{-3}$ .

Formula used:

The expression $a^{-n}$ is expressed as $\frac{1}{a^n}$ where a is a nonzero real number and n is a positive integer.

Calculation:

Consider the expression $4^{-3}$ .

Recall that expression $a^{-n}$ is expressed as $\frac{1}{a^n}$ where a is a nonzero real number and n is a positive integer.

Apply it,

  $\begin{array}{c}{4}^{-3}=\frac{1}{4^3}\\ =\frac{1}{64}\end{array}$

Thus, the simplified form of the expression $4^{-3}$ is $\frac{1}{64}$ .