Numbers: glossary

Powers

The 'fifth power of 3' simply means the number you get when you multiply 3 together five times. So it is -
3 x 3 x 3 x 3 x 3
- which equals 243.

This can also be written 3 where the small means 'to the fifth power'.

The 'first power' of a number is always equal to itself. So the first power of 3 equals 3. The 'second power' means the same as the square of a number. So the second power of 3 equals 9. The 'third power' is another way of saying the cube of a number.

Here are some of the powers of three -
3 = 3
3 = 3 x 3 = 9
3 = 3 x 3 x 3 = 27
3 = 3 x 3 x 3 x 3 = 81
3 = 3 x 3 x 3 x 3 x 3 = 243

The 'zeroth power' of any number always equals one, so 3 = 1.

The easiest powers to work out are the powers of ten -
10 = 1
10 = 10
10 = 100
10 = 1000
10 = 10000
10 = 100000
10 = 1000000
10 = 10000000
...

It is easy to see how this pattern continues.

Powers of ten have a special use for writing very big numbers. For example, the speed at which light travels is about 300,000,000 metres/second. But it is much easier to write -
3 x 10 metres/second.
- 10 tells us the number of zeros after the 3.