# Powers

The 'fifth power of 3' simply means the number you get when you multiply 3 together five times. So it is –

3 × 3 × 3 × 3 × 3

– which equals 243.

This can also be written 3^{5} where the small ^{5} 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^{1} = 3

3^{2} = 3 × 3 = 9

3^{3} = 3 × 3 × 3 = 27

3^{4} = 3 × 3 × 3 × 3 = 81

3^{5} = 3 × 3 × 3 × 3 × 3 = 243

The 'zeroth power' of any number always equals one, so 3^{0} = 1.

The easiest powers to work out are the powers of ten –

10^{0} = 1

10^{1} = 10

10^{2} = 100

10^{3} = 1000

10^{4} = 10000

10^{5} = 100000

10^{6} = 1000000

10^{7} = 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 × 10^{8} metres/second.

– 10^{8} tells us the number of zeros after the 3.

See also powers of two.

Based on the book *Numbers: Facts, Figures & Fiction*.