How to Use Power of a Quotient Rule for Exponents

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How to Divide Exponents using the Quotient Rule

The exponent rule for dividing exponential terms together is called the Quotient Rule. The Quotient Rule for Exponents states that when dividing exponential terms together with the same base, you keep the base the same and then subtract the exponents. If the exponential terms have multiple bases, then you treat each base like a common term. That means that only the bases that are the same will be divided with each other.

Common Core Standard: 8.EE.A.1

Basic Topics:

Return To: Home, 8th Grade

A Short Guide for Solving Quotient Rule Examples

What is the quotient rule for exponents anyway? The rule for dividing exponential terms together is known as the Quotient Rule. The rule for How to Divide Exponents expresses that while dividing exponential terms together with a similar base, you keep the base and subtract the exponents. On the off chance that the exponential terms have different bases, you treat each base like a like term. That means that only bases that are like terms will have their exponents subtracted from each other.

4 Quick Steps for Dividing Exponents with the Same Base

Identify the terms that have the same base.
If the bases are the same, you will subtract the exponents of the bases together.
If the bases are different, you will keep the exponents separate.
If an exponents is negative, be sure to include the negative when subtracting.

Quotient Rule Practice Problems Quiz

Watch Quotient Rule for Exponents Video Explanation

Watch our free video on how to Divide Exponents. This video shows how to solve problems that are on our free exponents dividing exponents with same base worksheet that you can get by submitting your email above.

Watch the free video on How to Divide Exponents on YouTube here: Quotient Rule for Exponents

Video Transcript:

This video is about the quotient rule of exponents. You can download the quotient rule exponents worksheet we use in this video for free by clicking on the link in the description below.

Here we are at the first problem on our quotient rule for exponents worksheet. Now if you look at the first problem, the first problem gives us 8 to the fourth divided by 8 squared and that’s what this fraction bar means – that means to divide. In order to show you how this works, what we’re going to do is, I’m going to write out 8 to the fourth which would be 8 times 8 times 8 or 8, 4 times, divided by 8 squared which would be 8 times 8 or – 8 times. Now anytime you’re dividing you can cancel. Whatever you have on top we’re going to cancel from the bottom. We have 1 8 on top which cancels one on bottom one on top which cancels one on bottom. What we’re left with is 8 times 8 which is equivalent or equal to 8 squared, and that’s going to be our answer.

If you look at our original problem, we have 8 to the fourth divided by 8 squared and you end up with 8 to the second power. A shortcut instead of having to do this middle step would be to subtract the exponents. If you take 8 to the 4th minus 2, we’re taking the top 1 minus the bottom 1, we will get the same answer, 8 squared. You can use this shortcut anytime you are using the quotient rule exponents.

Our next problem on the exponent quotient rule worksheet has two separate bases and I will show you how to solve these when you are given two separate bases. If you look at number 6, we have 3 to the 13th 5 to the seventh divided by 3 to the fifth 5 to the fourth. When we simplify this using the exponent quotient rule we’re going to keep the like terms together. We’re going to use our rule or a shortcut that we learned in the first problem which is to subtract the exponents. Then we will have a separate term which this time has a base of 5. Our first part we use the base of 3 our second part we’re going to use the base of 5. We will do 5 to the 7 minus 4 because that’s the exponent on top. When we simplify this we will do keep the base of 3 and then 13 minus 5 which is 8 and then for the second term we will keep the base which is 5 and then 7 minus 4 will be our exponent which is 3. That’s going to be our solution.

The last problem we’re going to review for the quotient exponent rule on our exponents rules worksheet involves a negative exponent. In the case of this problem we have a base of 7. We’re going to keep the base of 7 then we have a 3 exponent on top and then we’re being subtracted by a negative 7. You will keep the 3 then you will do – because we’re still being subtracted but it’s being subtracted by a negative 7. You have to include the negative in your subtraction. It’s 3 minus a negative 7 anytime you have two negatives together. It’s like 3 minus a negative or 2 negatives they become a positive and typically what I’ll do is I’ll rewrite it into a problem that looks like that. Now our two negatives become a plus now we have 7 to the 3 plus 7 which is 7 to the 10th power and that’s going to be our answer. You can try all the practice problems by downloading the free quotient law of exponents worksheet above.