Powers and Roots
A power tells you to multiply a number by itself.
For example, 53 means 5 x 5 x 5 which is 125.
24 means 2 x 2 x 2 x 2 which is 16.
It is a short way of writing out calculations.
For example, 33 x 42 = 3 x 3 x 3 x 4 x 4 = 432
A root is the opposite of a power.
- means 'what number do you square to get 4?'
The answer is 2.
- means 'what number do you cube (multiply by itself 3 times) to get 27?'
The answer is 3.
Rules of indices
There are several rules that you will need to know.
When you multiply indices of the same number you add the powers.
For example: 54 x 53 = 54 + 3 = 57
When you divide indices of the same number you subtract the powers.
Indices outside a bracket multiply.
For example: (32) 4 = 32 x 4 = 38
Negative indices mean reciprocal, i.e. 'one over...' or 'put on the bottom of a fraction'.
When the power is a fraction the top of the fraction (numerator) is a power and the bottom of the fraction…