1.1 Rule 1 – Multiplying with powers

If you want to multiply a³ by a² this can be written as:

Comparing the powers shows that the sum of the original powers (3 and 2) equals the power in the answer.

This works with any powers, both positive and negative, where the base number (a) is the same. So, the rule can be generalised as:

Here’s an example with both positive and negative indices.

Or using the rule 1:

This is a much quicker way to the answer.

This idea can be extended to include division, as you will see in the next section.