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Powers and roots

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# Powers

9 is a square number.
3 × 3 = 9
3 × 3 can also be written as 32. This is pronounced "3 squared".

8 is a cube number.
2 × 2 × 2 = 8
2 × 2 × 2 can also be written as 23, which is pronounced "2 cubed".

## Index form

The notation 32 and 23 is known as index form. The small digit is called the index number or power.

You have already seen that 32 = 3 × 3 = 9, and that 23 = 2 × 2 × 2 = 8.

Similarly, 54 (five to the power of 4) = 5 × 5 × 5 × 5 = 625
and 35 (three to the power of 5) = 3 × 3 × 3 × 3 × 3 = 243.

The index number tells you how many times to multiply the numbers together.

• 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 is has been multiplied 'to the power of'.

For example:

72 is 'seven squared',
33 is 'three cubed',
37 is 'three to the power of seven',
45 is 'four to the power of five'.

Question

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

 43 4 × 4 × 4 64 27 2 × 2 × 2 × 2 × 2 × 2 × 2 72 7 × 7 53 24 65