How to Divide Powers (Mathematics Lesson)
Dividing Powers
To divide powers, subtract the exponents from each other.
This is a law of exponents.
How to Divide Powers
Dividing powers is easy.
An Example Question
Use the law of exponents to divide the powers below.
Check that the bases of the powers are the same. In our example, the bases are both 2.
Find the exponent of the first power. In our example, the first power has an exponent of 5.
Find the exponent of the second power. In our example, the second power has an exponent of 3.
Subtract the exponents from Step 2 (5 and 3) from each other.
Make the answer from Step 3 (2) the exponent of the base of the powers that have been divided.
We have divided the powers from each other.
Understanding Dividing Powers
Let us look at the rule for dividing powers:

We are dividing powers. 2^{m}, 2^{n} and 2^{m  n} are powers.

The base in each power is 2. This law of exponents only applies when the bases are the same.

The exponents in each power are m, n and m  n. This law of exponents applies even when the exponents are different.
Dividing Powers As a Fraction
A division can be written as a fraction.
A Real Example of How to Divide Powers
The slider below shows another real example of how to divide powers.
Interactive Test
showHere's a second test on the dividing powers.
Here's a third test on dividing powers.
Beware
The Bases Must Be The Same
The law of exponents discussed here only works when the bases are the same.
The division below cannot be simplified, and must be left as it is:
Top Tip
0, 1 and Negative Exponents
When subtracting exponents, don't worry if the resulting exponent is 0, 1 or negative.
The relevant laws of exponents are:
 2^{0} = 1
 2^{1} = 2
 2^{  n} = 1 / 2^{n}