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Home » Exponents »
Negative and Zero Exponents

# Negative Exponents and Zero Exponents

## The Rule for Negative Exponents:

## TIP:

## Examples

## Any number (except 0) to the zero power is equal to 1.

## Example 1

## Example 2

## Example 3

## Example 4

## Practice Problems

## Answer Key

## You Might Also Like These Exponent Lessons:

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So far in this unit, you've learned how to simplify monomial expressions with positive exponents. Now we are going to study two more aspects of monomials: those that have **negative exponents** and those that have **zero as an exponent**.

I am going to let you investigate to see if you can come up with the rule on your own! Take a look at the following problems and see if you can determine the pattern.

Can you figure out the rule? If not, here it is...

The expression a^{-n} is the reciprocal of a^{n}

A **reciprocal** is when you "flip a fraction".

Examples:

The reciprocal of 3/4 is 4/3.

The reciprocal of 5 is 1/5. (You can make a whole number a fraction by putting a one in the denominator: 5 = 5/1)

***An easy rule to remember is: if the number is in the numerator (top), move it to the denominator (bottom). If the number is in the denominator, move it to the numerator!

Let's take a look at a couple of examples:

Now let's quickly take a look at monomials that contain the exponent 0.

Not too hard, is it? Let's look at a couple of example problems and then you can practice a few.

****Since 2/3 is in parenthesis, we must apply the power of a quotient property and raise both the 2 and 3 to the negative 2 power.**

First take the reciprocal to get rid of the negative exponent.

Then raise (3/2) to the second power.

Now, it's going to get a little more tough.

One more example.

Yes, I know that's a lot of examples to comprehend. My goal was to start easy and progress to harder problems. Are you ready to try a few on your own?

So, how did you do? Are you ready to move onto Scientifc Notation?

**Exponents Unit:**

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