4 Tips for Mastering Product Rules for Exponents
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How to Multiply Exponents using the Product Rule
The exponent rule for multiplying exponential terms together is called the Product Rule. The Product Rule states that when multiplying exponential terms together with the same base, you keep the base the same and then add the exponents. If the exponential terms have multiple bases, then you treat each base like a common term. That means that only the bases that are the same will be multiplied together.
Common Core Standard: 8.EE.A.1
A Guide for Multiplying Exponents with Variables
The rule for multiplying exponential terms together is known as the Product Rule. In order to multiply exponents you should increase exponential terms together with a similar base, you keep the base the equivalent and add the exponents. On the off chance that the exponential terms have different bases, you treat each base like a like term. That means that only like terms will be added together.
4 Steps for Multiply Exponents with the Same Base
- Identify the terms that have the same base.
- If the bases are the same, you will add the exponents of the bases together.
- If the bases are different, you will keep the exponents separate.
- If an exponents is negative, be sure to include the negative when adding.
Product Rule Practice Problems Quiz
Watch the Product Rule for Exponents Video Explanation
Watch our free video on how to Multiply Exponents. This video shows how to solve problems that are on our free Product Rule Exponents worksheet that you can get by submitting your email above.
Watch the free video on How to Multiply Exponents on YouTube here: Product Rule for Exponents
This video is about exponent product rule. You can download our product rule for exponents worksheet by clicking on the link in the description below.
Here we are at number one. Number one says we’re going to multiply 8 to the 4th times 8 to the 11th. In terms of this problem when we have 8 to the 4th, what that really is saying is 8 times 8 times 8 times 8, and then we have 8 to the 11th. What 8th to the 11th is saying is we’re multiplying 8 to the 4th times 8 to the 11th or we have 11 8’s. If you look at our problem we have 8 to the 4th, there are 4 8s and then we have multiplied times 8 to the 11th, which are 11 8s. When you multiply all those together you have to figure out how many eights you are going to end up with. What we’re going to do is we’re going to count 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 8. Our final answer will be 8 to the 15th power.
You can skip this step if you know the product rule exponents. You will notice that what we did was we counted up all of the 8 but instead of having to do that you could have just added the exponents. If you look back to our original problem of 8 to the 4th times 8 to the 11th. If you just do 4 plus 11 you will get the same answer 8 to the 15th. The shortcut for using the product rule for exponents is to just add the exponents together as long as they have the same base.
Our next example gives us 4 to the 8th times the four to the fifth eight to the third. Now we learned in our first example the rules for multiplying exponents can be just he add the exponents. What we’re going to do is we’re going to take the fours and we’re going to add the exponents together and then we’re going to take the base of eight and rewrite it underneath. Now the reason we don’t write the two together is because the bases are different. This is a base of four and they can get multiplied or combine together and this has a base of eight and it cannot go with the fours. If we had hypothetically another eight here we could have multiplied the aides together but we don’t have another eight. We just leave the eight by itself when using the shortcut we’re going to add the exponents to the four. We will do four to the eight plus five which is four to the 13th power and then we have this eight to the third that is getting combined with nothing else. It will just stay 8 to the third and that is our answer.
The final example that we’re going to go over shows when we have a negative exponent. Just because we have a negative exponent does not mean the product rule of exponents changes. We still have a base of seven. We know that because the base of seven for both of these we’re going to add them together. We’re going to keep the base and then we’re going to add negative three plus the exponent of 17. When you add negative 3 plus 17 you get 14 and that’s gonna be your answer. The key takeaway here is that just because we have a negative exponent does not change the rule, the rules stay the same. You can try all the practice problems by downloading the free product rule of exponents worksheet above.
Product Rule for Exponents
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