Problem 63 - Prealgebra

Question

Find the value of each expression. $$12^{2}$$

Step-by-Step Solution

Answer

The value of \(12^2\) is 144.

Step 1: Understanding the Expression

The expression given is \(12^2\). This means that the number 12 is raised to the power of 2, which is equivalent to multiplying 12 by itself.

Step 2: Applying Power Rule

To calculate \(12^2\), apply the power rule which states that any number \(a\) raised to the power of \(b\) is the multiplication of \(a\) by itself \(b\) times.

Step 3: Performing the Multiplication

Multiply 12 by itself: \(12 \times 12 = 144\). This multiplication results in the value of the expression, which is 144.

Key Concepts

Power Rule for Exponents

The power rule is a fundamental principle in prealgebra that deals with exponents. When you see a number like \(12^2\), it means the base (12) is being multiplied by itself (2 times, in this case). In simple terms:

• The base is the number that is being multiplied.
• The exponent (or power) tells you how many times to multiply the base by itself.

In our example of \(12^2\), the number 12 is multiplied by 12. Understanding the power rule is crucial for handling any expressions that involve exponents. It helps you quickly determine what calculations are needed to simplify or evaluate the expression.

Multiplication in Exponents

When dealing with exponents, multiplication is a key operation. Consider \(12^2\), where you perform multiplication as follows:

• First, identify the base and the exponent. Here, the base is 12, and the exponent is 2.
• Next, use the exponent to determine how many times to multiply the base by itself.

This gives us: \(12 \times 12 = 144\). Multiplication allows us to work out the result of exponent expressions easily. It's important to remember that mastering basic multiplication helps in evaluating exponents effectively.

Prealgebra and Exponents

Prealgebra sets the foundation for more advanced math topics by focusing on basic principles like exponent rules. Exponents, such as \(12^2\), appear frequently and understanding them is essential for your mathematical development. Some key points include:

• Comprehending the notation and meaning of exponents (e.g., \(12^2\) means 12 is multiplied by itself).
• Practicing calculations: Use multiplication skills to solve exponential expressions.
• Recognizing patterns: As you get used to exponents, you'll start to see patterns that can simplify calculations.

Being comfortable with these concepts in prealgebra makes transitioning to algebra smoother, where you'll encounter more complex expressions and equations that also use exponents.