2.4 Negative exponents

The same approach used to understand what zero as a power means can also be used for negative exponents or powers.

This time showing as a fraction, simplifying and using the rules for powers with the same base. This gives:

So,

Now, using the rule for dividing numbers with the same base:

Putting these two results together gives:

In the same way, means , or , which is equivalent to .

Since is 25 and is , in maths 5^-2 is said to be the reciprocal of 5². So, negative powers represent the reciprocal of the same positive power.

Negative powers of ten then enable small numbers to be shown using scientific notation. Before that though you will practise understanding and writing negative powers in the next activity.