**Understanding Exponents (Powers)** *KS3 Revision*

## What you need to know

**Things to remember:**

- “Exponent” is a fancy way of saying “power”.
- Exponents and powers tell us how many times we need to multiply a number by itself.

An exponent is a number written to the top right of a number and tells us how many times we multiply a number by itself.

6^2 = 6\times 6

6^3 = 6\times 6\times 6

6^4= 6\times 6\times 6\times 3

0 a special power, because the answer is always 1!

5^0 = 1

123^0 = 1

23.4^0 = 1

\pi^0 = 1

*What is the value of 5^3?*

* *

5^3=5\times5\times5=25\times5=125

* *

*What is the value of 4^3+2^5?*

* *

4^3=4\times4\times4=16\times4=64

2^5=2\times2\times2 \times2 \times2 =4\times2 \times2 \times2 =8\times2 \times2 =16\times2 =32

4^3+2^5 =64+32=96

Exponent are mainly used to write things in a quicker way, so instead of writing lots of multiplications we can just write it with powers

2\times2\times2\times2\times2\times2\times8\times8\times8\times8=2^6\times8^4

Powers are also useful for computing. Try typing \times2 into your calculator 70 times.

- This is going to take a long time; typing 2^{70} is much quicker.
- Your calculator probably doesn’t have enough memory to let you type it 70 times!

## Example Questions

**Question 1:** Write the following using powers:

7\times7\times7\times2\times2\times2\times9\times9\times9

7\times7\times7\times2\times2\times2\times9\times9\times9

7^3\times2^3\times9^3

**Question 2:** What is the value of 5^4\times3^2?

5^4=5\times5\times5\times5=25\times5\times5=125\times5=625

3^2=3\times3=9

5^4\times3^2 =625\times9=5625