Question

Compute \(5^3\). Write your answer in the box.

Short answer

125

Step-by-step solution

- Understand Exponentiation

Exponentiation involves raising a base number to a certain power. Here, the base number is 5 and the exponent is 3. This means you need to multiply the base number by itself as many times as indicated by the exponent.

- Break Down the Multiplication

You need to compute \(5^3\). This can be broken down into \(5 \times 5 \times 5\).

- Perform the Multiplication

First, multiply the first two numbers: \(5 \times 5 = 25\). Next, multiply the result by the remaining base number: \(25 \times 5 = 125\).

- Write the Final Answer

After completing the multiplication, the result of \(5^3\) is 125.

Key concepts

Understanding the Base Number

The base number is a fundamental concept in exponentiation. In the expression \(5^3\), the base number is 5. It is the number that will be multiplied by itself repeatedly. Here's a way to think about it:

• The base number is like the foundation or starting point.
• In any exponential expression, the base number is always the number written at the bottom.
• It shows what number will be used in the multiplication process.

For example, in \(5^3\), you start with the base number 5 and repeatedly multiply it by itself, driven by what the exponent indicates. This foundational understanding helps in breaking down and solving exponential problems with confidence.

Defining the Exponent

The exponent determines how many times the base number will be multiplied by itself. In \(5^3\), the exponent is 3. This means we will multiply the base number 5 by itself three times.

• The exponent is always the smaller number written as a superscript.
• It tells you the 'power' to which the base number is raised.
• Think of the exponent as a count of how many times to use the base number in the multiplication.

For example, the exponent 3 in \(5^3\) means we calculate the multiplication this way: \(5 \times 5 \times 5\). Remember, the exponent reflects the number of times the base number is a factor.

Performing the Multiplication

Let's dive into how multiplication works in exponentiation. When calculating \(5^3\), we need to multiply the number 5 by itself three times. Here's a step-by-step breakdown:

• First, write down the base number the number of times indicated by the exponent: \(5 \times 5 \times 5\).
• Start with the first multiplication: \(5 \times 5 = 25\).
• Then, take the result and multiply it by the base number again: \(25 \times 5 = 125\).

Hence, the result of \(5^3\) is 125. This method can be applied to any exponentiation problem, helping you solve them efficiently step by step.
Multiplication in the context of exponents always follows this rule: continue multiplying by the base number until you've done so as many times as the exponent indicates.