Division with Exponent Revision | KS3 Maths Resources

## 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!

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

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

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

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

## KS3 Maths Revision Cards

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## Example Questions

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

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

## KS3 Maths Revision Cards

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