2.3 Zero as a power?

The easiest way to investigate whether a number raised to the power of zero means anything mathematically, is to look at an example.

Here, start with . Using the rules from the last section about dividing numbers with the same base number this gives us:

.

So, is the same as

However, another way of looking at is by writing this as a fraction and then simplifying it.

This gives:

But , this means that:

So, although 10⁰, that is ‘10 multiplied by itself zero times’ does not make any practical sense, mathematically this has the value of 1. You can use a similar argument to show that any number to the power zero has a value of 1. For example,

.

You could check these on your calculator now if you would like to confirm this is correct.

Remembering this rule will be very useful if you continue your study of maths, science or technology based subjects, so it is not just an interesting diversion!

Now let’s get back to scientific notation and how to show small numbers in this format. The first thing to do is though is to look at negative powers, or exponents, in the next section.