# What are Negative Exponents?

##### 1 Answer

**Negative exponents** are an extension of the initial exponent concept.

To understand **negative exponents** ,

first review what we mean by **positive** (integer) **exponents**

What do we mean when we write something like:

One definition would be that

Note that using this definition

i.e.

Suppose you know the value of

but you would like to know the value of

For example suppose you knew that

Is there a faster way than multiplying

Yes.

If we note that

we can simply divide

In general if we know that the value of

and we want to know the value of

we can simply divide k by n^(p-q)

With this in mind what is the value of

We know that

so

That is

As a final example consider the descending powers of 3 in the following, noting that with each line down the result is decreased by dividing the current value by 3