Exponent with Powers Revision | KS3 Maths Resources

## What you need to know

Things to remember:

• If we put a power on something that already has a power, we just multiply them!

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

$$3^4=3\times3\times3\times3$$

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

$$a^2=a\times a$$

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

Simplify $(a^5)^3$ by writing as a single power.

So, what do we know about these powers?

$$a^5= a\times a\times a\times a\times a$$

But, what about the cube power? Well, we do it in the same way, but instead multiply a letter or number by itself 3 times, we are multiply $a^5$ by itself 3 times.

$$(a^5)^3=a^5\times a^5 \times a^5$$

But, we know how to deal with powers when we are multiplying them… we just add!

$$a^5\times a^5 \times a^5=a^{5+5+5}$$

Remember though, if we are adding the same number multiple times, we can write it as a multiplication with how many numbers there are!

$$a^{5+5+5}=a^{5\times3}$$

And now, all we have to do is multiply these numbers!

$$a^{5\times3}=a^{15}$$

$$(a^5)^3 = a^{15}$$

The important stage here is the one in bold, it shows us that all we have to do is multiply the powers together!

$$(3^2)^6 = 3^{2\times6}=3^{12}$$

$$(6^2)^7 = 6^{2\times7}=6^{14}$$

$$(x^5)^9 = x^{5\times9}=x^{45}$$

$$(n^3)^y = n^{3\times y}=n^{3y}$$

$$(a^b)^c = a^{b\times c}=a^{bc}$$

## KS3 Maths Revision Cards

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## Example Questions

$$(5^7)^3=5^{7\times3}=5^{21}$$

$$(a^8)^x=a^{8\times x}=a^{8x}$$

## KS3 Maths Revision Cards

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