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How to Divide Exponents Download Article Understanding this simple power rule Co-authored by David Jia
Last Updated: March 14, 2026 References
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Understanding the Basics
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This article was co-authored by David Jia. David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor’s degree in Business Administration. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math. This article has been viewed 198,593 times.
Dividing expressions that have exponents is easier than it looks. As long as you're working with the same base, all you have to do is subtract the values of the exponents from each other and keep the base the same.[1]X Expert Source David JiaAcademic TutorExpert Interview If you're struggling with this, jump down to Step 1 for easy instructions on getting through the process.
How to Divide Exponents with the Same Base
If you have two exponents with the same base, just subtract the exponent you are dividing by from the exponent you are dividing.
Steps
Part 1 Part 1 of 2:
Understanding the Basics
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1 Write down the problem. The most simple version of this problem will be in the form of ma ÷ mb. In this case, you're working with the problem m8 ÷ m2. Write it down.
2 Subtract the second exponent from the first. The second exponent is 2 and the first is 8. So, you can rewrite the problem as m8-2.[2]XResearch source Advertisement
3 State your final answer. Since 8 - 2 = 6, your final answer is m6. It's that simple. If you're not working with a variable and have an actual number in the base, such as 2, then you would have to do the math (26 = 64) to finish solving the problem.[3]XResearch source
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Going the Extra Mile
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1 Make sure that each expression has the same base. If you're working with different bases, then you cannot divide the exponents. Here's what you need to know:
If you're working with a problem with variables, such as m6 ÷ x4, then there's nothing more you can do to simplify it.
However, if the bases are numbers and not variables, you may be able to manipulate them so you end up with the same base. For example, in the problem, 23 ÷ 41, you first have to make both bases be "2." All you do is rewrite 4 as 22 and do the math: 23 ÷ 22 = 21, or 2.
You can only do this, however, if you can turn the larger base into an expression of squared numbers to make it have the same base as the first.
2 Divide expressions with multiple variables. If you have an expression with multiple variables, then you just have to divide the exponents from each identical base to get your final answer. Here's how you do it:[4]XResearch source
x6y3z2 ÷ x4y3z =
x6-4y3-3z2-1 =
x2z
3 Divide expressions with coefficients. As long as you're working with the same base, it's no problem if each expression has a different coefficient. Just divide the exponents as you normally would and divide the first coefficient by the second. Here's how:[5]XResearch source
6x4 ÷ 3x2 =
6/3x4-2 =
2x2
4 Divide expressions with negative exponents. To divide expressions with negative exponents, all you have to do is move the base to the other side of the fraction line. So, if you have 3-4 in the numerator of a fraction, you'll have to move it to the denominator. Here are two examples:[6]XResearch source
Example 1:
x-3/x-7 =
x7/x3 =
x7-3 =
x4
Example 2:
3x-2y/xy =
3y/(x2 * xy) =
3y/x3y =
3/x3
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Question How can I divide a by b, if both have exponent c? Donagan Top Answerer It would be the fraction (a/b) raised to the power of c. Thanks! We're glad this was helpful.Thank you for your feedback. If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow Yes No Not Helpful 11 Helpful 21
Question How do I divide a positive number with a positive exponent by a positive number with a negative exponent? Community Answer First of all, the two positive numbers (the bases) have to be the same. If they are, you subtract the exponent in the denominator from the exponent in the numerator. If the denominator's exponent is negative, you treat it as if it were positive and add it to the numerator's exponent. Thus, x^3 ÷ x^(-1) = x^4. Thanks! We're glad this was helpful.Thank you for your feedback. If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow Yes No Not Helpful 8 Helpful 20
Question What is 400 divided by 10^3? Community Answer 400 / 10³ = 400 / 1000 = 0.4. Thanks! We're glad this was helpful.Thank you for your feedback. If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow Yes No Not Helpful 8 Helpful 14
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Don't worry if you get it wrong! Keep trying! Thanks Helpful 2 Not Helpful 0
If you have a calculator it is usually a good idea to check your answer. Calculate both the sum and your answer to it to check that they are the same. Thanks Helpful 1 Not Helpful 0
If you are confused, you can always ask your parents or someone that knows the subject well enough to assist you. Thanks Helpful 1 Not Helpful 0
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Co-authored by: David Jia Math Tutor This article was co-authored by David Jia. David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor’s degree in Business Administration. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math. This article has been viewed 198,593 times. 12 votes - 82% Co-authors: 22Updated: March 14, 2026 Views: 198,593 Categories: Multiplication and DivisionArticle SummaryX
To divide exponents with the same base, start by subtracting the second exponent from the first. For example, if your problem is m to the 4th power divided by m to the 2nd power, then you would subtract 2 from 4 in order to get 2. That means your final answer is m to the 2nd power. Alternatively, if your problem is 2 to the 5th power divided by 2 to the 2nd power, subtract 2 from 5 to get an answer of 2 to the 3rd power. To learn how to divide expressions with coefficients, keep reading!Did this summary help you?YesNo
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Download Article Understanding this simple power rule Co-authored by David Jia 
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Co-authored by: David Jia Math Tutor This article was co-authored by David Jia. David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor’s degree in Business Administration. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math. This article has been viewed 198,593 times. 12 votes - 82% Co-authors: 22 Updated: March 14, 2026 Views: 198,593 Categories: Multiplication and Division Article SummaryX
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1 Write down the problem. The most simple version of this problem will be in the form of ma ÷ mb. In this case, you're working with the problem m8 ÷ m2. Write it down. 
2 Subtract the second exponent from the first. The second exponent is 2 and the first is 8. So, you can rewrite the problem as m8-2.[2] Advertisement 
3 State your final answer. Since 8 - 2 = 6, your final answer is m6. It's that simple. If you're not working with a variable and have an actual number in the base, such as 2, then you would have to do the math (26 = 64) to finish solving the problem.[3] Advertisement 
1 Make sure that each expression has the same base. If you're working with different bases, then you cannot divide the exponents. Here's what you need to know: 
2 Divide expressions with multiple variables. If you have an expression with multiple variables, then you just have to divide the exponents from each identical base to get your final answer. Here's how you do it:[4] 
3 Divide expressions with coefficients. As long as you're working with the same base, it's no problem if each expression has a different coefficient. Just divide the exponents as you normally would and divide the first coefficient by the second. Here's how:[5] 
4 Divide expressions with negative exponents. To divide expressions with negative exponents, all you have to do is move the base to the other side of the fraction line. So, if you have 3-4 in the numerator of a fraction, you'll have to move it to the denominator. Here are two examples:[6] 
Donagan Top Answerer It would be the fraction (a/b) raised to the power of c. Thanks! We're glad this was helpful. Thank you for your feedback. If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow Yes No Not Helpful 11 Helpful 21 
Community Answer First of all, the two positive numbers (the bases) have to be the same. If they are, you subtract the exponent in the denominator from the exponent in the numerator. If the denominator's exponent is negative, you treat it as if it were positive and add it to the numerator's exponent. Thus, x^3 ÷ x^(-1) = x^4. Thanks! We're glad this was helpful. Thank you for your feedback. If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow Yes No Not Helpful 8 Helpful 20