Problem 15 - Beginning and Intermediate Algebra

Question

Evaluate. \(4^{2}\)

Step-by-Step Solution

Answer

The value of \(4^2\) is 16.

Step 1: Understand the Expression

The given expression is \(4^2\). This is a power expression, where the base is 4 and the exponent is 2.

Step 2: Apply the Exponent Rule

Recall that \(a^b\) means multiplying the base \(a\) by itself \(b\) times. So, \(4^2\) means you multiply 4 by itself once.

Step 3: Perform the Multiplication

Calculate 4 times 4. So, \(4 \times 4 = 16\).

Step 4: Write the Final Answer

Therefore, the value of \(4^2\) is 16.

Key Concepts

Base and Exponent

When you look at a power expression like \(4^{2}\), you encounter two important parts: the base and the exponent. The base is the number 4, and the exponent is the number 2. The base is the number that you will multiply by itself. The exponent tells you how many times you will use the base in the multiplication.

In other words:

• Base: The number you want to multiply.
• Exponent: How many times you multiply the base by itself.

Understanding these terms is essential when working with power expressions, as they dictate how the expression is calculated.

Power Expressions

Power expressions, like \(4^{2}\), represent a way to write repeated multiplication in a shorter form. Instead of writing \(4 \times 4\), you represent this operation with a base raised to an exponent. This shorthand makes it easier to handle larger numbers and more complex calculations.

The concept of power expressions is based on a rule:

• \(a^b\) represents multiplying the number \(a\) by itself \(b\) times.

For \(4^2\), this would be 4 multiplied by 4, which simplifies calculations and keeps the math tidy and organized. Becoming familiar with power expressions can greatly simplify mathematical problems.

Multiplication of Numbers

Once you understand the parts of a power expression, you can easily perform the multiplication it represents. For \(4^{2}\), you multiply 4 by itself, which is \(4 \times 4\). Multiplying these two numbers gives you the result 16.

This multiplication is straightforward:

• First 4: The base, which starts the operation.
• Second 4: The base used again as indicated by the exponent.
• Product: The result of the multiplication, which is 16.

Remember, multiplication in power expressions follows the same rules as regular multiplication, providing a direct pathway to the final result.