Squares, cubes and higher powers are shown as small digits called indices. The opposite of squaring and cubing are called square root and cube root. There are more rules we can use with indices.

Part of

How can we work out ?

so

There are twos from and twos from , so altogether there are twos.

The index can be found from adding the indices and . Remember, this only works when we are multiplying powers of the same number together.

In general:

The rule also works for other numbers, so:

If you divide by you see that some of the s cancel:

So .

There are twos from and twos from , so after dividing there are twos. The index can be found from subtracting the indices, . Remember, this only works when we are dividing powers of the same number.

In general, .

The rule also works for other numbers: