Problem 11 - Elementary and Intermediate Algebra

Question

Simplify. $$ 3^{2} $$

Step-by-Step Solution

Answer

The simplified form of \(3^2\) is 9.

Step 1: Identify the Base and Exponent

Recognize that in the expression \(3^2\), the base is 3 and the exponent is 2.

Step 2: Understand the Exponentiation

Exponentiation means that the base (3) is multiplied by itself as many times as indicated by the exponent (2). So, \(3^2\) means \(3\) multiplied by itself 2 times.

Step 3: Perform the Multiplication

Multiply the base by itself the number of times indicated by the exponent: \(3 \times 3 = 9\).

Step 4: Write the Simplified Form

The simplified form of \(3^2\) is 9.

Key Concepts

Base and Exponent

In mathematics, exponentiation is a fundamental operation. It involves two key components: the base and the exponent. The base is the number that is being multiplied, and the exponent indicates how many times the base is multiplied by itself.
For example, in the expression \(3^2\), the base is 3 and the exponent is 2. This tells us that we need to multiply the base (3) by itself two times. Understanding the role of both the base and the exponent is crucial in solving exponentiation problems effectively.

Multiplication

Once you understand the base and exponent, the next step is to perform the multiplication.

• The exponent of 2 means that the base will be multiplied by itself once.

Let's look at this in the expression \(3^2\):
Here, you take the base, which is 3, and multiply it by itself:
\(3 \times 3\)
After performing the multiplication, you get the result:
\(3 \times 3 = 9\). This intermediate step is crucial for simplifying the expression correctly.

Simplified Form

Simplifying an exponentiation expression means finding its most concise form. The simplified form is often a single number or a more compact expression.

For \(3^2\):

• First, identify the base (3) and the exponent (2).
• Second, multiply the base by itself (\(3 \times 3\)).
• Lastly, write the final result of the multiplication (9).

The simplified form of \(3^2\) is, therefore, 9. Simplification helps in quickly understanding and using the expression in further mathematical calculations.