How to Divide Powers in Algebra (Mathematics Lesson)
Dividing Powers in Algebra
To divide powers, subtract the exponents from each other.
This is a law of exponents.
How to Divide Powers in Algebra
Dividing powers in algebra 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 x.
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 in Algebra
Let us look at the rule for dividing powers in algebra:

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

The base in each power is a. 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 in Algebra As an Algebraic Fraction
A division in algebra can be written as an algebraic fraction.
A Real Example of How to Divide Powers in Algebra
The slider below shows another real example of how to divide powers in algebra.
Curriculum
Interactive Test
showHere's a second test on the dividing powers in algebra.
Here's a third test on dividing powers in algebra.
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:
 a^{0} = 1
 a^{1} = a
 a^{  n} = 1 / a^{n}