4 Steps for Mastering our Negative Exponents Worksheet

Get the free Negative Exponents Worksheet and other resources for teaching & understanding solving our Negative Exponents Worksheet

A Short Guide of the Rules for Negative Exponents

Negative Exponents refer to bases that are raised to a power that is negative. In order to simplify bases raised to negative exponents, you must make the exponents positive. The shortcut for changing negative exponents into positive exponents, is to flip the term with a negative exponent over the fraction line. Once the term has been flipped over the fraction line, the exponent becomes positive.

If there is nothing left on one side of the fraction line, you use the number one as a place holder. If there are any other like terms, you must simplify the problem by either multiplying or dividing the exponents of the like terms.

Common Core Standard: 8.EE.A.1

Return To: Home, 8th Grade

Explaining Negative Exponents Rules

Read the explanation below to learn how to get rid of negative exponents.

Negative Exponents allude to bases that are raised to a power that is negative. To solve bases raised to negative powers, you should make the powers positive. Changing negative powers into positive powers, is to flip the term with a negative power over the division line. When the term has been flipped over the division line, the power becomes positive.

On the off chance that there is nothing left on one side of the division line, you use one as a place holder. On the off chance that there are some other like terms, you should combine them issue by combining the like terms.

4 Steps for Solving Negative Exponents Examples

Whenever a term has a negative exponent, it is not simplified.
You must make all of the negative exponents positive.
Flip any term with a negative exponent over the fraction bar.
When you flip the term over the negative exponent, you make the exponent positive.

Negative Exponents Practice Problems Quiz

Watch the video on how to Solve Negative Exponents

Watch our free video on how to solve Negative Exponents. This video shows how to solve problems that are on our free Negative Exponent worksheet that you can get by submitting your email above. The Negative Exponents Rules shown in the video will work on any problem that involve Negative Exponents.

Watch the free Negative Exponents video on YouTube here: Negative Exponents Worksheet

Video Transcript:

This video is about using the negative exponent rule. We’re going to use our negative exponent rule worksheet to show you a couple example problems showing you how to do negative exponents.

Here is the first problem in our negative exponents practice worksheet. We are given five to the negative ninth. Now in order to simplify each expression with a negative exponent you have to make the exponent positive. In the case of number one this exponent here of negative nine needs to be turned into a positive nine. The way you make this exponent positive is that you have to flip it on to the other side of the fraction bar. That might not make any sense at first but you have to remember that all whole numbers are written over 1. 5 to the negative ninth actually has a 1 or is being divided by one underneath of it, even though we don’t write it every single time. In order to make this exponent positive you have to take your term here, which is 5 to the negative ninth, and you have to move the entire thing to the bottom of the fraction bar. After you do that the exponent will become positive.

We take 5 to the negative ninth, we can write our fraction bar. If we want it becomes 5 you keep the base and then you make the exponent positive 5 to the positive ninth our term on top is gone but we have to include a placeholder. The placeholder we’re going to use is the number one because one divided by five to the ninth doesn’t change the actual value of the term. This will be our answer and it shows how to make a negative exponent positive.

Moving on to number three on our negative exponents rule we have 1 over 7 to the negative twentieth. Now the same process we used in number one also works in number three except instead of moving our term to the bottom, like we did, our term is already on the bottom. We’re going to move it to the top what we’re trying to do is we’re trying to make the exponent positive. This negative 20 needs to turn into a positive 20. We’re going to take our term 7 to the negative 20th and we’re going to move it to the top of this term, to the top of the fraction bar. It will become seven to the positive twentieth. Anytime you flip a number or term over the fraction bar sign on the exponent changes. Now our negative twenty becomes positive and then on bottom we have to use a placeholder to keep the number in correct numerical terms. And we’re going to use one now seven to the 20th power divided by one is just seven to the 20th power and that’s our answer.

The last example for the negative power rule that we’re going to do is a little bit trickier we’re given X to the negative third divided by X to the fourth. The first thing we need to do is we need to get rid of this negative three. We have to make it positive, so just like in the other examples, the way you do that is you flip it over the fraction bar. We will write X to the fourth because it’s on the bottom so it stays on the bottom. We don’t change anything about that we just moved it over and now we have also X to the positive third, which now has been moved to the bottom. We took our term here we move the whole thing to the bottom and we rewrote it right next to X to the fourth. Now on top we have to use 1 as a placeholder.

The next step is we have to simplify X to the 4 times X to the 3rd. When we do that we’re just going to multiply them together. And you will remember that when you multiply terms with exponents you add the exponents. We’ll keep the base of X and then we’ll do 4 plus 3 which is 7 and 1 over X to the positive 7th is our solution. You can try the practice problems by downloading the free negative exponents worksheets above.