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Understanding this simple power rule
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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. 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
-
Write down the problem. The most simple version of this problem will be in the form of m a ÷ m b . In this case, you're working with the problem m 8 ÷ m 2 . Write it down. -
Subtract the second exponent from the first. The second exponent is 2 and the first is 8. So, you can rewrite the problem as m 8-2 . [1] X Research sourceAdvertisement -
State your final answer. Since 8 - 2 = 6, your final answer is m 6 . 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 (2 6 = 64) to finish solving the problem. [2] X Research source
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-
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 m 6 ÷ x 4 , 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, 2 3
÷ 4 1
, you first have to make both bases be "2." All you do is rewrite 4 as 2 2
and do the math: 2 3
÷ 2 2
= 2 1
, 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.
-
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: [3] X Research source- x 6 y 3 z 2 ÷ x 4 y 3 z =
- x 6-4 y 3-3 z 2-1 =
- x 2 z
-
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: [4] X Research source- 6x 4 ÷ 3x 2 =
- 6/3x 4-2 =
- 2x 2
-
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: [5] X Research source- Example 1
:
- x -3 /x -7 =
- x 7 /x 3 =
- x 7-3 =
- x 4
- Example 2
:
- 3x -2 y/xy =
- 3y/(x 2 * xy) =
- 3y/x 3 y =
- 3/x 3
- Example 1
:
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Community Q&A
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QuestionHow can I divide a by b, if both have exponent c?Top AnswererIt would be the fraction (a/b) raised to the power of c.
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QuestionHow do I divide a positive number with a positive exponent by a positive number with a negative exponent?Community AnswerFirst 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.
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QuestionWhat is 400 divided by 10^3?Community Answer400 / 10³ = 400 / 1000 = 0.4.
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Tips
- Don't worry if you get it wrong! Keep trying!Thanks
- 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
- If you are confused, you can always ask your parents or someone that knows the subject well enough to assist you.Thanks
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References
- ↑ https://www.dummies.com/how-to/content/how-to-divide-exponents.html
- ↑ https://www.mathsisfun.com/algebra/variables-exponents-multiply.html
- ↑ https://www.mathsisfun.com/algebra/variables-exponents-multiply.html
- ↑ https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:rational-exponents-radicals/x2f8bb11595b61c86:exponent-properties-review/v/multiplying-and-dividing-powers-with-integer-exponents
- ↑ https://www.purplemath.com/modules/simpexpo2.htm
About This Article
Article Summary
X
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!
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