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Chapter 2: Problem 340

In the following exercises, simplify each expression. $$ 4^{3} $$

Short Answer

Expert verified
64

Step by step solution

01

Understand the Exponent

The expression given is \(4^3\). This means that the number 4 is being multiplied by itself a total of 3 times.
02

Multiply the Base Repeatedly

Start with the base number, which is 4. Multiply it by itself the number of times indicated by the exponent, which is 3. So you have \(4 \times 4 \times 4\).
03

Perform the Calculations

First, calculate \(4 \times 4 = 16\). Then, multiply that result by 4 again: \(16 \times 4 = 64\).
04

Write the Simplified Expression

The simplified expression for \(4^3\) is 64.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Exponents
Exponents are a shorthand way to show repeated multiplication of the same number. Imagine needing to multiply the number 4 by itself three times. Instead of writing it out as 4 x 4 x 4, you can use an exponent to simplify the expression to 43.

Here's a quick breakdown:
  • The base is the number being multiplied.
  • The exponent tells you how many times to multiply the base by itself.

So, in our example, 43 means you multiply 4 by itself a total of 3 times.
Multiplication
Multiplication is the process of adding a number to itself a specific number of times. When it comes to exponents, multiplication plays a key role. For example, in the expression 43:

  • Start by multiplying 4 by 4 to get 16.
  • Next, multiply that result (16) by 4 again to get 64.

So, each step of multiplication brings you closer to the simplified result of the expression.
Base and Exponent
Understanding the components of an exponent is crucial. The two main parts are the base and the exponent. Let's break them down for the expression 43:
  • The base is the number being multiplied, which is 4 in this case.
  • The exponent tells us how many times to multiply the base by itself, which is 3 here.

When you understand these two parts, you can easily decode any expression with exponents. Just multiply the base by itself however many times the exponent says to, and you'll get the simplified result.

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Most popular questions from this chapter

In the following exercises, solve each equation using the addition property of equality. $$ u-6=24 $$

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Write the equation \(y-5=21\) in words. Then make up a word problem for this equation.

In the following exercises, solve each equation using the addition property of equality. $$ 18=q-72 $$

In the following exercises, simplify, using the order of operations. $$ (1+4)^{2} $$
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