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Chapter 1: Problem 14

Find the value of each exponential expression. $$ 5^{3} $$

Short Answer

Expert verified
The value of \(5^{3}\) is 125.

Step by step solution

01

Understand the Base and Exponent

Recognize that in the expression \(5^{3}\), the base is 5 and the exponent is 3. This notation means that you need to multiply the base by itself as many times as indicated by the exponent.
02

Multiply Repeatedly

Multiply the base by itself 3 times: \(5 \times 5 \times 5\).
03

Calculate the Product

Carry out the multiplication sequentially: \(5 \times 5 = 25\) and then \(25 \times 5 = 125\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Base and Exponent
To understand exponential expressions, we need to first grasp what 'base' and 'exponent' mean. In the expression \(5^{3}\), the base is 5, and the exponent is 3.
The base is the main number that is being multiplied. The exponent tells us how many times to multiply the base by itself.
So for \(5^{3}\), this means you are multiplying 5 by itself 3 times.
This can be written as \(5 \times 5 \times 5\).
Recognizing the roles of the base and exponent is essential to solving these kinds of expressions.
Multiplication
Once you understand the base and exponent, the next step is to perform the multiplication.
From the previous example, we need to multiply the base (5) by itself as many times as the exponent (3) indicates.
So, we write it out as \(5 \times 5 \times 5\).
Here, we are performing the operation in steps:
  • First, multiply the first two numbers: \(5 \times 5\).
  • This gives us 25.
  • Next, take the result (25) and multiply by the base once more: \(25 \times 5\).
  • This final multiplication results in 125.
Breaking it down step-by-step helps make the process clear and manageable.
Calculation
To finalize the solution, you need to carry out the actual calculation by sequentially performing the multiplications.
From our above steps, we have:
  • First multiplication: \(5 \times 5 = 25\)
  • Second multiplication: \(25 \times 5 = 125\)
So, the value of \(5^{3}\) is 125.
This step-by-step approach ensures each part of the multiplication is accurate and easy to follow.
If you follow these precise steps, you can calculate any exponential expression with confidence and accuracy.

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