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# 1.2 Rule 2 – Dividing with powers

This time let’s look at a5 divided by a2, which can be written as:

This time the difference between the powers (5 and 2) is the same as the power in the final result – giving Rule 2:

Equation label: (Rule 2)

Thus

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

(Note when you divide by a fraction it is the same as multiplying by the inverted fraction. If you want to revise fractions try another of our badged courses – Succeed with Maths Part 2).

Or using Rule 2:

It is important to remember that Rules 1 and 2 only work if the powers involve the same base number, for example, you can’t apply them to a3 × b2 or a7 − b5.

There are occasions when you will encounter a power of a power – the next section looks at this situation.