First you need to understand what an index (or power) is. It’s just a compact way of writing a number multiplied by itself a number of times. For example:

3⁴ = 3x3x3x3 and a² = axa.

If two indices have the same base number (big number at the bottom) then they can be multiplied easily.

For example, if you wanted to find 2³ x 2⁴:

First you can write this out in full.

2³ x 2⁴ = (2x2x2) x (2x2x2x2)

This is just 2 multiplied by itself 7 times which we can write as 2⁷.

The trick to multiplying indices without writing them out in full each time is just to add the powers together. In the example above the powers are 3 and 4.

3+4 = 7 so 2³ x 2⁴ = 2⁷.

Dividing indices is very similar, only instead of adding the powers you subtract them.

E.g. Find 2⁶ / 2²:

These have the same base number (2) so we’re good to go.

Subtract the powers:

6 - 2 = 4

This gives you the power of 2 in the answer:
2⁶ / 2² = 2⁴

That’s all there is to multiplying and dividing indices. When multiplying, add the powers. When dividing, subtract!

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