1.3 Rule 3 – Powers of powers

You know that a² = a × a.

This can be extended to powers of powers.

So,

Using Rule 1 gives:

This time the product (3 × 2) of the original powers is the same as the power in result. So, rule 3 can be stated as:

Again, this rule works for positive and negative indices.

For example,

So far you have looked at powers that are all integers, however fractional powers are also very common. These will be the subject of the next section.