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Chapter 1: Problem 44

Write each expression without using exponents. $$(4 x)^{3}$$

Short Answer

Expert verified
The simplified expression of \( (4x)^3 \) without using an exponent is \(64x \times x \times x\)

Step by step solution

01

Understand the Problem

The problem is asking to write the expression \( (4x)^3 \) without using exponents. This means the expression must be simplified such that it contains repeated multiplication but does not include any exponent.
02

Break Down the Exponent

The power of 3 means that the base \(4x\) multiplies by itself three times. So, start by writing \( (4x)^3 \) as \(4x \times 4x \times 4x\).
03

Simplify the Expression

Next, simplify this expression. The multiplication operation is associative, which means it does not matter in what order the numbers are multiplied. Therefore, simplify this as follows: First, multiply the numerical parts: 4*4*4 equals 64. Second, multiply the variable parts: \(x*x*x\) equals \(x^3\). Thus, \(4x \times 4x \times 4x\) simplifies to \(64x^3\)
04

Check Your Result

Since the problem asked to present the result without using exponents, we will detail the variable part with multiplication instead. Hence, \(64x^3\) becomes \(64x \times x \times x\). However, keep in mind that this is just the detailed version of the same result.

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