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Chapter 0: Problem 23

Evaluate each expression. $$ 4^{2} $$

Short Answer

Expert verified
16

Step by step solution

01

Identify the Base and Exponent

The expression is given as \(4^2\). In this expression, the base is 4 and the exponent is 2.
02

Understand What the Exponent Means

The exponent tells us how many times to multiply the base by itself. So, \(4^2\) means we have to multiply 4 by itself 2 times.
03

Perform the Multiplication

Multiply the base by itself as many times as indicated by the exponent: \(4 \times 4 = 16\)
04

Write the Final Answer

After performing the multiplication, we get the final answer: \(4^2 = 16\).

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Key Concepts

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

base and exponent
In any exponential expression, such as \(4^2\), there are two main components: the base and the exponent. The base is the number that gets multiplied by itself. Here, the base is 4.
The exponent, 2 in this case, indicates how many times the base is used as a factor.
Exponential expressions are a convenient way to show repeated multiplication.
By learning to identify the base and the exponent, you can easily understand and solve any exponential problem.
Let's take another example: \(3^3\). Here, the base is 3, and the exponent is 3. This means we multiply 3 by itself three times, so \(3 \times 3 \times 3 = 27\).
exponential notation
Exponential notation is a mathematical method for writing longer multiplication sequences in a simpler form.
Instead of writing out 4 multiplied by 4, as in \(4 \times 4\), we use exponential notation to write it more compactly as \(4^2\).
This notation has wide applications in mathematics, from simplifying calculations to understanding scientific principles.
The expression \(b^n\) means you multiply the base \(b\) by itself \(n\) times.
For instance, \(2^5\) is the same as writing \(2 \times 2 \times 2 \times 2 \times 2 \), which equals 32.
multiplication skills
Strong multiplication skills are essential when working with exponents.
They help you quickly solve exponential expressions and understand more complex mathematical concepts.
Mastering multiplication tables and practicing mental multiplication can make things easier.
For instance, knowing that \(4 \times 4 = 16\) without using a calculator is very useful.
Work on multiplication with smaller numbers first, and then gradually tackle more complex problems as you grow confident.
Good multiplication skills ensure that you can evaluate exponents accurately and efficiently.

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Most popular questions from this chapter

Use an inequality symbol to write each statement. $$ 6+7 \text { is not equal to }-13 $$

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