Problem 28 - Algebra 1

Question

Evaluate the power. $$ 8^{2} $$

Step-by-Step Solution

Answer

The result of \(8^{2}\) is 64.

Step 1: Understand the exponent notation

In the expression \(8^{2}\), 8 is the base and 2 is the exponent. The expression reads '8 to the power of 2' which means 8 is multiplied by itself 2 times.

Step 2: Perform the multiplication

Since the exponent is 2, it means the base 8 is multiplied by itself. So, the calculation we need to perform is \(8*8\).

Step 3: Computation and Final Solution

By performing the multiplication \(8*8\), we get 64. That's our final answer for the expression \(8^{2}\).

Key Concepts

Base and Exponent

At the heart of exponentiation lies the concept of the base and exponent. When we see an expression like \(8^{2}\), it's good to break it down into its components:

• Base: This is the number that will be multiplied by itself. In this case, the base is 8.
• Exponent: This tells us how many times to multiply the base by itself. Here, the exponent is 2.

Together, these form the term "8 to the power of 2". The arrangement indicates how the base is utilized. Starting with these basic definitions will make understanding exponentiation less intimidating.
At its core, it’s a straightforward repeated multiplication process. Recognizing the base and exponent sets the groundwork for solving any power expression.

Multiplication

In exponentiation, multiplication is the pivotal process that transforms the base into the complete power expression. Looking at our problem, \(8^{2}\), we see that the exponent 2 indicates we need to multiply the base 8 by itself 2 times.
So, the multiplication process involves performing the operation \(8 \times 8\).

• This is a simple multiplication problem where the same number is repeatedly used.
• Multiplication here means combining equal groups, and in exponents, these groups are formed by the base itself.

Breaking it down in these terms helps clarify the role of multiplication in finding powers, and practicing such problems solidifies one's understanding of the multiplication aspect in exponentiation.

Power Evaluation

The process of power evaluation brings us to the solution of an exponent expression. After understanding the base and exponent and performing the necessary multiplication, we arrive at the stage of evaluation.
To evaluate \(8^{2}\), we executed the multiplication \(8 \times 8\) to get 64.
Here’s what happens in this step:

• The multiplication results in a single value, representing the power of the base with the given exponent.
• This step results in the final answer, simplifying the exponent expression to a plain numerical value.
• Evaluation confirms the computational effect of repeatedly applying the base through multiplication.

This final phase demonstrates how repeated multiplication powers the initial base, culminating in a solution. Each evaluation exercise reaffirms the fundamental principles learned in earlier steps and proves to be key in mastering exponentiation.