# Power numbers

Topic Progress:

The power of a number says how many times to use the number in a multiplication. It is written as a small number to the right and above the base number. An example is 82 = 8 × 8 = 64. (Another name for power is index or exponent).

There are some exponents which have special names:

Squared – this is when the exponent is 2, so:

6 squared = 6² = 6 x 6 =36

Cubed – this is when the exponent is 3, so:

8 cubed = 8³ = 8 x 8 x 8 = 512

To the power of – if there is no special name, then we describe the number as ‘a number to the power of’, so:

8 to the power of 5 = 85 = 8 x 8 x 8 x 8 x 8 = 32,768

## Powers of ten

You will often see units with the power symbol, both positive and negative attached to the number 10. This indicates the size of the unit. For example if the unit is associated with 10³ then the unit needs to be multiplied by 1000 (10 x 10 x 10).

If the power symbol is negative, for instance 10-3, in this example the -3 indicates we need to divide the number by 10³ (ie divide by 1000).

These multiplications and divisions by 10 are known as the prefix.

## Metric units prefix

A prefix is used if the number of units we are working with are either very large or very small. By using a prefix we can more easily understand the measure of the unit.

For example in the UK, the National Grid distributes electricity at 400000 V or 275000 V, to make it easier to read we use the prefix k, so we write 400 kV or 275 kV. k is equivalent to 1,000.

In electrical work we might see a very low current of 0.000005 A, to make it easier to read we use the prefix μ, so we write 5 μA. μ is equivalent to 0.00000 (5 zeroes after decimal point).

### Table of common prefixes

Text Symbol Factor Power
giga G 1000000000 109
mega M 1000000 106
kilo k 1000 103
(none) (none) 1
milli m 0.001 10−3
micro μ 0.000001 10−6
nano n 0.000000001 10−9