# Why is a number raised to a negative power the reciprocal of that number?

##### 1 Answer

**Simple answer:**

We'll do this by working backwards.

How can you make

Well, you divide by 2:

How can you make

Well, you divide by 2:

How can you make

Well, you divide by 2:

How can you make

Well, you divide by 2:

**Proof why this should be the case**

The definition of the reciprocal is: "a number's reciprocal multiplied by that number should give you 1".

Let

Or you can also say the following:

Since both of these are equal to

Divide both sides by

And you have your proof.