**Division with Exponent** *KS3 Revision*

## What you need to know

**Things to remember:**

- When dividing terms with the same base number, we just need to subtract the second exponent from the first.
- We don’t write the exponent if it is just 1.

** **

“Exponents” is just another way of saying “powers” and tells us how many times we have to multiply a number or letter by itself.

3^4=3\times3\times3\times3

5^6=5\times5 \times5 \times5 \times5 \times5

a^2=a\times a

n^5=n\times n\times n\times n\times n

** **

So, as we can see, we use powers as a quick way of writing lots of multiplications! But, what if we need to divide by some exponents?

*Write 2^5\div2^2 as a single power.*

Let’s start by looking at each piece individually.

2^5=2\times2\times2 \times2 \times2=32

2^2=2\times2=4

So, that means, *2^5\div2^2=32\div4 but we can write that as*

* *

32\div4=8

But, we can now write 8 as a power of 2.

8=2^3

Which gives us our original question as a single power!

2^5\div2^2=2^3

Notice how 5-2=3. When we divide terms with powers, as long as the base numbers are the same, we can just subtract the second number from the first!

5^8\div5^4=5^{8-4}=8^4

6^2\div6^5=6^{2-5}=6^{-3}

c^{15}\div c^8=c^{15-8}=c^7

a^5\div a^{-2}=a^{5--2}= a^{5+2}=a^7

## Example Questions

**Question 1:** Write 5^7\div5^{-3} as a single power.

5^7\div 5^{-3}=5^{7--3}= 5^{7+3}=a^{10}

**Question 2:** Write a^8\div b^{11} as a single power.

We can’t, the bases letters aren’t the same!!!!