# Index laws for multiplication and division

## Multiplication

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 and . Remember, this only works when we are multiplying powers of the same number together.

In general:

### Examples

The rule also works for other numbers, so:

## Division

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

Dividing numbers with powers

Five 2s are divided by three 2s

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, .

### Example

The rule also works for other numbers:

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