How to Divide Power-terms (Exponents) in Algebra

Hello! Today, we’re going to learn about dividing power-terms in algebra. This might sound a little tricky at first, but don’t worry—we’ll break it down into simple steps and use some examples to help you understand.

What Are Power-Terms?

Before we dive into dividing power-terms, let’s quickly review what power-terms are.

Power-terms, also known as exponents, are a way to express repeated multiplication of the same number. They consist of a base and an exponent. The base is the number being multiplied, and the exponent tells us how many times to multiply the base by itself.

Basic Components of Power-Terms

1. Base: The number that is being multiplied.
2. Exponent: The small number written above and to the right of the base, indicating how many times to multiply the base.

For example, in the power-term 2³:

• The base is 2.
• The exponent is 3.

This means you multiply 2 by itself 3 times: 2 × 2 × 2 = 8.

The Rule for Dividing Power-Terms

When we divide power-terms with the same base (the same number being multiplied), we subtract the exponents.

The rule is:

Here, a is the base, and m and n are the exponents.

Let’s Break It Down with an Example

Example 1:

1. Identify the Base and Exponents:
   • The base is 8.
   • The exponents are 5 and 3.
2. Apply the Rule:
   • Subtract the exponent in the denominator (bottom) from the exponent in the numerator (top): 5 – 3.
3. Simplify:
   • .
4. Calculate the Result:
   • .

So, .

More Examples

Example 2:

1. Identify the Base and Exponents:
   • The base is 10.
   • The exponents are 4 and 2.
2. Apply the Rule:
   • Subtract the exponent in the denominator from the exponent in the numerator: 4 – 2.
3. Simplify:
   • .
4. Calculate the Result:
   • .

So,

Example 3: ​

1. Identify the Base and Exponents:
   • The base is 5.
   • The exponents are 7 and 3.
2. Apply the Rule:
   • Subtract the exponent in the denominator from the exponent in the numerator: 7 – 3.
3. Simplify:
   • .
4. Calculate the Result:
   • .

So, .

Common Mistakes to Avoid

1. Forgetting to Subtract the Exponents:
   • Remember, when dividing power-terms with the same base, you subtract the exponents. Don’t add them or multiply them!
2. Using Different Bases:
   • The rule only applies to power-terms with the same base. For example, ​ cannot be simplified using this rule because the bases (4 and 3) are different.
3. Misinterpreting the Rule:
   • Make sure you are comfortable with the rule and apply it correctly.

Practice Problems

Now it’s your turn to practice! Try simplifying these expressions on your own:

1. ​
2. ​
3. ​​
4. ​

Check your answers below to see how you did.

Answers to Practice Problems

Great job! Keep practicing, and you’ll master the concept of dividing power-terms in no time. Happy learning!