Properties of Exponents
There are several properties of exponents, but two are especially important to consider when we are factoring. They are:
- Product of Powers Property
- Quotient of Powers Property
Product of Powers Property
This property states that when you multiply two powers having the same base, you add the exponents.
Let's take a look at an example:
Let's take a look at an example:
Why do we add the exponents? If we break it down,
Therefore, when we multiply these together, we get
The video below shows a few more examples. Be careful to pay attention to examples 3 and 4. They have coefficients in front of the variables.
4 5 Rules of Exponents Product of Powers Property by sarakarch: https://www.youtube.com/watch?v=iDU2q1YycSA
Quotient of Powers Property
This property states that when you divide two powers having the same base, you subtract the exponents.
Let's take a look at an example:
Let's take a look at an example:
Why do we subtract the exponents? If we break it down,
Therefore, when we divide, we get
The video below shows a few more examples. Be careful to pay attention to examples 3 and 4. They have coefficients in front of the variables.
4 5 Rules of Exponents Quotient of Powers Property by sarakarch: https://www.youtube.com/watch?v=NFJeLzuAc0M
Practice:
Use the following website to practice using the Product of Powers Property:
https://www.ixl.com/math/grade-8/multiplication-with-exponents
Use the following website to practice using the Quotient of Powers Property:
https://www.ixl.com/math/grade-8/division-with-exponents
https://www.ixl.com/math/grade-8/multiplication-with-exponents
Use the following website to practice using the Quotient of Powers Property:
https://www.ixl.com/math/grade-8/division-with-exponents
When you have become a master at using the Product of Powers and Quotient of Powers Properties, go back and retake the pre-test. You should score 80% or higher before moving on.
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