Dividing Exponents: Everything You Need to Know
Are you ready to become a master of dividing exponents?
(Need help with Negative Exponents, click here for our super easy 3-step explanation)
Let’s start with the following key question about dividing exponents:
How can you divide powers (or exponents) with the same base?
Note that the following method works when the base is either a number or a variable (the following lesson guide will show examples of both)
Dividing Exponents Example
Let’s start with a simple example: what is 5^7 divided by 5^4?
Start by rewriting the fraction in expanded form as follows (you won’t have to do this every time, but we’ll do it now to help you understand the rule, which we’ll get to later.)
Notice how there are repeat values in the numerator and the denominator.
Since any non-zero value divided by itself is equal to one, you can cancel out these repeats as follows:
Doing this allows you to rewrite the above fraction in simplified form, as follows:
Finally, you can rewrite 5 x 5 x 5 as 5^3 and you have finished the problem.
5^7 divided by 5^4 equals 5^3
Dividing Exponents Rule
Did you notice a relationship between all of the exponents in the example above?
Notice that 5^7 divided by 5^4 equals 5^3. Also notice that 7 - 4 = 3
This relationship applies to dividing exponents with the same base whether the base is a number or a variable:
Whenever you divide two exponents with the same base, you can simplify by subtracting the value of the exponent in the denominator by the value of the exponent in the numerator.
Here are a few examples applying the rule:
Dividing Exponents Rule Example (Variable Base)
Dividing Exponents Rule Example (Numerical Base)
Dividing exponents with the same base is as simple as that!
If you still need help, check out this free Dividing Exponents video lesson:
Video: Dividing Exponents Explained in 3 Minutes!
Dividing Exponents Practice Worksheet and Answer Key
Are you looking for some extra dividing exponents practice?
Click the link below to download your free Dividing Exponents PDF Worksheet and Answer Key!
>>> Click here to get your free Dividing Exponents Worksheet.
(answer key included)
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By Anthony Persico
Anthony is the content crafter and head educator for YouTube's MashUp Math . You can often find me happily developing animated math lessons to share on my YouTube channel . Or spending way too much time at the gym or playing on my phone.
