Exploring Exponents: 0 and Negatives as Exponents

Contributor: Briana Pincherri. Lesson ID: 11245

You may have had a "negative" experience with exponents, with "zero" desire to learn them. Watch these simple videos and try some easy examples, and you'll become an exponent of using . . . exponents!


Expressions and Equations, Pre-Algebra

learning style
personality style
Lion, Otter
Grade Level
Middle School (6-8)
Lesson Type
Quick Query

Lesson Plan - Get It!

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  • If you have an exponent of 0, doesn't that just make your answer automatically 0?
  • What if you have a negative exponent with a positive base?
  • Does that make the answer negative, or does it do something else?

Let's find out!

At this point, you should be familiar with the terms base and exponent.

Remember that the base is the number you will be multiplying by itself, and the exponent is the little tiny number that tells you how many times you will multiply the base by itself.

  • Now, what happens if the exponent is 0?

Let's take a look at this video, What Do You Do With a Zero Exponent? Virtual Nerds: Real Help:

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As you saw, any number to the 0 power is 1. It doesn't matter if it is x0, 40, or even 1,000,00010. Each of these will be equal to 1!

Great! We now know how to handle positive exponents and exponents of 0.

  • But what about when we see a negative exponent?
  • What do we do with that?

2-3 = ?

When we have a negative exponent, we want to do the inverse (or opposite). Typically, when we see an exponent, we know we are going to be multiplying.

  • So, what is the opposite of multiplication?

It's division. The negative exponent simply tells us how many times to divide by the base.

While it may sound tricky, I think you will like it. You are about to see that the negative exponent just means you are going to:

  1. decide what the positive exponent would look like
  2. take the reciprocal of the base with the above positive exponent

I have a feeling it will make more sense by looking at the example:

2-3 =

Now think, what would the positive exponent look like?


23 =

Well, it would look like this! Now, take the reciprocal and you are finished.


2-3 =





As you can see in this example, when you have negative exponents, you simply find the reciprocal and include the positive version of the exponent.

In the answer above, you can now do the math to find the final answer to be 1/8 (because 2 x 2 x 2 = 8).

Here are a few more examples to take a look at:










































  • Now, how about you try a few in the Got It? section?

You can feel free to look back at these examples at any point as a guide.

Remember, when dealing with negative exponents, you can simply decide what the positive version of the exponent would be and use it in the reciprocal.

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