Division law for indices
Home learning focus
In this lesson you will learn how to divide indices.
This lesson includes:
- a video
- a worksheet with answers
The notation 3² (three squared) and 2³ (two cubed) is known as index form. The small digit is called the index number or power.
3² = 3 × 3 = 9
2³ = 2 × 2 × 2 = 8
The index number tells you how many times the number should be multiplied.
Index laws for division
Dividing numbers with powers
If you divide 2⁵ by 2³ you will see that some of the 2s cancel.
There are 5 twos from 2⁵ and 3 twos from 2³, so after dividing there are 2 twos remaining. The index 2 can be found by subtracting the indices, 5 - 3 = 2.
So 2⁵ ÷ 2³ = 2².
In general, the rule is: 2ᵐ ÷ 2ⁿ = 2⁽ᵐ⁻ⁿ⁾.
Remember, this only works when you are dividing powers of the same base number.
2⁵ ÷ 2² = 2⁽⁵⁻²⁾ = 2³
5¹⁰ ÷ 5³ = 5⁽¹⁰⁻³⁾ = 5⁷
45⁹ ÷ 45⁴ = 45⁽⁹⁻⁴⁾ = 45⁵
a⁸ ÷ a² = a⁶
30a²b ÷ 5ab² = 6ab⁻¹
Dividing powers with the same base
Now test your understanding and knowledge of dividing powers with the same base by working through these worksheets from Beyond. Questions are grouped by difficulty either as Bronze, Silver or Gold so aim to get as far as you can! There is also a challenge to complete at the end. Write your answers on a piece of paper.
There's more to learn
Have a look at these other resources around the BBC and the web.