Problem 4 - Elementary Algebra

Question

For exercises 1-80, evaluate. $$ 5^{3} $$

Step-by-Step Solution

Answer

The value of \(5^3\) is 125.

Step 1: Understand the Problem

The task is to evaluate the expression involving the exponentiation of 5 raised to the power of 3.

Step 2: Recall the Exponentiation Rule

Exponentiation means multiplying the base by itself as many times as indicated by the exponent. Here, the base is 5 and the exponent is 3.

Step 3: Perform the Multiplication

Multiply the base 5 by itself according to the exponent: \(5^3 = 5 \times 5 \times 5\)

Step 4: Calculate

Calculate the multiplication step-by-step: \(5 \times 5 = 25\), then multiply the result by the base again: \(25 \times 5 = 125\)

Step 5: Final Answer

Therefore, the value of \(5^3\) is 125.

Key Concepts

Base and Exponent

In exponentiation, there are two main components: the base and the exponent. The base represents the number that is being multiplied. The exponent tells us how many times the base is multiplied by itself. When looking at the expression, such as in the exercise, we have 5 raised to the power of 3. Here, 5 is the base and 3 is the exponent. This means we will multiply 5 by itself a total of 3 times. Understanding these key terms is crucial for correctly evaluating exponentiation problems.

Multiplication

Multiplication is a fundamental math operation that you use when working with exponentiation. For an expression like 5 raised to the power of 3, you perform the multiplication step by step:
- First, you multiply 5 by 5, which gives 25.
- Then, you take the result, which is 25, and multiply it by 5 again. This gives 125.
As you can see, the multiplication process follows from evaluating how many times the base (5) is being used, as determined by the exponent (3). Every correct step of multiplication ensures an accurate final result.

Step-by-Step Solution

Let's break down the solution to the problem step-by-step:

Step 1: Understand that you need to evaluate the expression involving exponentiation, here, 5 raised to the power of 3.

Step 2: Recall the exponentiation rule: the base is multiplied by itself as many times as indicated by the exponent.

Step 3: Start the multiplication: \(5^3 = 5 \times 5 \times 5\).

Step 4: Calculate sequentially: \(5 \times 5 = 25\), then multiply 25 by 5: \(25 \times 5 = 125\).

Step 5: State the final answer: \(5^3 = 125\).

By following this structured approach, you ensure that every step is clear and accurate, leading you to the correct evaluation of any exponentiation expression.