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 3⁵ 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 –
3¹ = 3
3² = 3 × 3 = 9
3³ = 3 × 3 × 3 = 27
3⁴ = 3 × 3 × 3 × 3 = 81
3⁵ = 3 × 3 × 3 × 3 × 3 = 243

The 'zeroth power' of any number always equals one, so 3⁰ = 1.

The easiest powers to work out are the powers of ten –
10⁰ = 1
10¹ = 10
10² = 100
10³ = 1000
10⁴ = 10000
10⁵ = 100000
10⁶ = 1000000
10⁷ = 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 × 10⁸ metres/second.
– 10⁸ tells us the number of zeros after the 3.

See also powers of two.

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