How to Multiply Exponents

Co-authored by David Jia

Last Updated: December 6, 2023

Exponents are a way to identify numbers that are being multiplied by themselves. They are often called powers . You will come across exponents frequently in algebra, so it is helpful to know how to work with these types of expressions. You can multiply exponential expressions just as you can multiply other numbers. If the exponents have the same base, you can use a shortcut to simplify and calculate; otherwise, multiplying exponential expressions is still a simple operation.

Method 1

Method 1 of 3:

Multiplying Exponents with the Same Base

Download Article

{"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/6\/6c\/Multiply-Exponents-Step-1-Version-3.jpg\/v4-460px-Multiply-Exponents-Step-1-Version-3.jpg","bigUrl":"\/images\/thumb\/6\/6c\/Multiply-Exponents-Step-1-Version-3.jpg\/aid2850587-v4-728px-Multiply-Exponents-Step-1-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}

1
Make sure the exponents have the same base. The base is the large number in the exponential expression. You can only use this method if the expressions you are multiplying have the same base.
- For example, you can use this method to multiply $5^{{2}}\times 5^{{3}}$ , because they both have the same base (5). On the other hand, you cannot use this method to multiply $5^{{2}}\times 2^{{3}}$ , because they have different bases (5 and 2).
{"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/e\/ea\/Multiply-Exponents-Step-2-Version-3.jpg\/v4-460px-Multiply-Exponents-Step-2-Version-3.jpg","bigUrl":"\/images\/thumb\/e\/ea\/Multiply-Exponents-Step-2-Version-3.jpg\/aid2850587-v4-728px-Multiply-Exponents-Step-2-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}

2
Add the exponents together. Rewrite the expression, keeping the same base but putting the sum of the original exponents as the new exponent. ^{[1]
X
Research source}
- For example, if you are multiplying $5^{{2}}\times 5^{{3}}$ , you would keep the base of 5, and add the exponents together:
  $5^{{2}}\times 5^{{3}}$
  $=5^{{2+3}}$
  $=5^{{5}}$
Advertisement
{"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/a\/aa\/Multiply-Exponents-Step-3-Version-3.jpg\/v4-460px-Multiply-Exponents-Step-3-Version-3.jpg","bigUrl":"\/images\/thumb\/a\/aa\/Multiply-Exponents-Step-3-Version-3.jpg\/aid2850587-v4-728px-Multiply-Exponents-Step-3-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}

3
Calculate the expression. An exponent tells you how many times to multiply a number by itself. ^{[2]
X
Research source} You can use a calculator to easily calculate an exponential expression, but you can also calculate by hand.
- For example $5^{{5}}=5\times 5\times 5\times 5\times 5$
  $5^{{5}}=3,125$
  So, $5^{{2}}\times 5^{{3}}=3,125$

Method 2

Method 2 of 3:

Multiplying Exponents with Different Bases

Download Article

{"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/8\/87\/Multiply-Exponents-Step-4-Version-3.jpg\/v4-460px-Multiply-Exponents-Step-4-Version-3.jpg","bigUrl":"\/images\/thumb\/8\/87\/Multiply-Exponents-Step-4-Version-3.jpg\/aid2850587-v4-728px-Multiply-Exponents-Step-4-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}

1
Calculate the first exponential expression. Since the exponents have different bases, there is no shortcut for multiplying them. Calculate the exponent using a calculator or by hand. Remember, an exponent tells you how many times to multiply a number by itself.
- For example, if you are multiplying $2^{{3}}\times 4^{{5}}$ , you should note that they do not have the same base. So, you will first calculate $2^{{3}}=2\times 2\times 2=8$ .
{"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/c\/c8\/Multiply-Exponents-Step-5-Version-3.jpg\/v4-460px-Multiply-Exponents-Step-5-Version-3.jpg","bigUrl":"\/images\/thumb\/c\/c8\/Multiply-Exponents-Step-5-Version-3.jpg\/aid2850587-v4-728px-Multiply-Exponents-Step-5-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}

2
Calculate the second exponential expression. Do this by multiplying the base number by itself however many times the exponent says.
- For example, $4^{{5}}=4\times 4\times 4\times 4\times 4=1024$
{"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/9\/97\/Multiply-Exponents-Step-6-Version-3.jpg\/v4-460px-Multiply-Exponents-Step-6-Version-3.jpg","bigUrl":"\/images\/thumb\/9\/97\/Multiply-Exponents-Step-6-Version-3.jpg\/aid2850587-v4-728px-Multiply-Exponents-Step-6-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}

Following the same example, your new problem becomes $8\times 1024$ .
{"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/b\/ba\/Multiply-Exponents-Step-7-Version-3.jpg\/v4-460px-Multiply-Exponents-Step-7-Version-3.jpg","bigUrl":"\/images\/thumb\/b\/ba\/Multiply-Exponents-Step-7-Version-3.jpg\/aid2850587-v4-728px-Multiply-Exponents-Step-7-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}

4
Multiply the two numbers. This will give you the final answer to the problem.
- For example: $8\times 1024=8192.$ So, $2^{{3}}\times 4^{{5}}=8,192$ .

Method 3

Method 3 of 3:

Multiplying Mixed Variables with Exponents

Download Article

{"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/9\/9d\/Multiply-Exponents-Step-8.jpg\/v4-460px-Multiply-Exponents-Step-8.jpg","bigUrl":"\/images\/thumb\/9\/9d\/Multiply-Exponents-Step-8.jpg\/aid2850587-v4-728px-Multiply-Exponents-Step-8.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}

1
Multiply the coefficients. Multiply these as you would any whole numbers. Move the number to the outside of the parentheses.
- For example, if multiplying $(2x^{{3}}y^{{5}})(8xy^{{4}})$ , you would first calculate $((2)x^{{3}}y^{{5}})((8)xy^{{4}})=16(x^{{3}}y^{{5}})(xy^{{4}})$ .
{"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/7\/7d\/Multiply-Exponents-Step-9.jpg\/v4-460px-Multiply-Exponents-Step-9.jpg","bigUrl":"\/images\/thumb\/7\/7d\/Multiply-Exponents-Step-9.jpg\/aid2850587-v4-728px-Multiply-Exponents-Step-9.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}

2
Add the exponents of the first variable. Make sure you are only adding the exponents of terms with the same base (variable). Don’t forget that if a variable shows no exponent, it is understood to have an exponent of 1. ^{[3]
X
Research source}
- For example:
  $16(x^{{3}}y^{{5}})(xy^{{4}})=16(x^{{3}})y^{{5}}(x)y^{{4}}=16(x^{{3+1}})y^{{5}}y^{{4}}=16(x^{{4}})y^{{5}}y^{{4}}$
{"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/e\/ec\/Multiply-Exponents-Step-10.jpg\/v4-460px-Multiply-Exponents-Step-10.jpg","bigUrl":"\/images\/thumb\/e\/ec\/Multiply-Exponents-Step-10.jpg\/aid2850587-v4-728px-Multiply-Exponents-Step-10.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}

3
Add the exponents of the remaining variables. Take care to add exponents with the same base, and don’t forget that variables with no exponents have an understood exponent of 1.
- For example:
  $16(x^{{4}})y^{{5}}y^{{4}}=16x^{{4}}y^{{5+4}}=16x^{{4}}y^{{9}}$

Video

Community Q&A

Search

Add New Question

Question

What is the solution for 3.5 x 10 to the fourth power?

Community Answer

10^4 = 10 x 10 x 10 x 10 = 10,000, so you are really multiplying 3.5 x 10,000. The shortcut is that, when 10 is raised to a certain power, the exponent tells you how many zeros. 10^4 = 1 followed by 4 zeros = 10,000. Thus, you can just move the decimal point to the right 4 spaces: 3.5 x 10^4 = 35,000.

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 1 Helpful 13
Question

How do I divide exponents that don't have the same base?

Community Answer

To learn how to divide exponents, you can read the following article: http://www.wikihow.com/Divide-Exponents

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 5 Helpful 9
Question

How do I write 0.0321 in scientific notation?

Donagan

Top Answerer

0.0321 = 3.21 x 10^(-2).

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 3 Helpful 13

See more answers

Ask a Question

200 characters left

Include your email address to get a message when this question is answered.

Submit

Tips

Any number or variable with an exponent of 0 is equal to 1. For example, $(5^{{0}})(x^{{0}})=(1)(1)=1$ .

Thanks
Helpful 0 Not Helpful 0

Submit a Tip

All tip submissions are carefully reviewed before being published

Name

Please provide your name and last initial

Submit

Thanks for submitting a tip for review!

[1]

[2]

[3]

Log in

How to Multiply Exponents

Steps

Multiplying Exponents with the Same Base

Multiplying Exponents with Different Bases

Multiplying Mixed Variables with Exponents

Video

Community Q&A

Tips

You Might Also Like

References

About This Article

Reader Success Stories

Did this article help you?

Quizzes

You Might Also Like

Featured Articles

Trending Articles

Featured Articles

Featured Articles

Watch Articles

Trending Articles

Quizzes

Explore Categories