# Powers

$${9}$$ is a square number.

$3 \times 3 = 9$

$$3 \times 3$$ can also be written as $$3^2$$. This is pronounced "$${3}$$ squared".

$${8}$$ is a cube number.

$2 \times 2 \times 2 = 8$

$$2 \times 2 \times 2$$ can also be written as $$2^3$$, which is pronounced "$${2}$$ cubed".

## Index form

The notation $$3^2$$ and $$2^3$$ is known as index form. The small digit is called the index number or power.

You have already seen that $$3^2 = 3 \times 3 = 9$$ and that $$2^3 = 2 \times 2 \times 2 = 8$$.

Similarly, $$5^4$$ (five to the power of $${4}$$) $$= 5 \times 5 \times 5 \times 5 = 625$$

and $$3^5$$ (three to the power of $${5}$$) $$= 3 \times 3 \times 3 \times 3 \times 3 = 243$$.

The index number tells you how many times the number should be multiplied.

• When the index number is two, the number has been squared.
• When the index number is three, the number has been cubed.
• When the index number is greater than three you say that it has been multiplied to the power of.

For example:

$$7^2$$ is 'seven squared'.

$$3^3$$ is 'three cubed'.

$$3^7$$ is 'three to the power of seven'.

$$4^5$$ is 'four to the power of five'.

Question

Look at the table and work out the answers. The first has been done for you.