1. Division Properties of Exponents
“I can use the properties of exponents to simplify numerical expressions.”
8.M.EE.01

2. Review
Simplify the following expressions:
3x・x2
(x2・y2)2
a2・a3・a5 2

3. Vocabulary
Power
Quotient
Numerator
Denominator 3

4. Quotient of Powers Property
To divide powers having the same base, you subtract the exponents.
Examples: 1)
What is the base?
Subtract the exponents!
Simplify
15, Final Solution

5. Quotient of Powers Property
To divide powers having the same base, you subtract the exponents.
Examples: 2)
What is the base?
k Subtract the exponents!
k Simplified Solution

6. Practice
Simplify the following expressions:

7. Power of a Quotient Property
To find a power of a quotient, find the power of both the numerator and the denominator and divide.
The exponent outside the parentheses is “distributed” to everything inside the parentheses.
Examples: 1)
What is the numerator?
What is the denominator?
Distribute the power!
Simplify and reduce.

8. ( ) Power of a Quotient Property Examples: 2 2) What is the numerator?
To find a power of a quotient, find the power of both the numerator and the denominator and divide.
The exponent outside the parentheses is “distributed” to everything inside the parentheses.
Examples:
( ) 2 2)
What is the numerator?
What is the denominator?
Why 3x2?
Distribute the power!
Simplify and reduce.

9. Power of a Quotient Property Examples:3)
What is the numerator?
What is the denominator?
Distribute the power!
Simplify and Reduce
Simplified Solution!

10. Practice
Simplify the following expressions:

11. Anything to the 0 power is equal to 1.

12. Practice
Simplify the following expressions:

13. A negative exponent means you move the base to the other side of the fraction and make the exponent positive.
Notice that the base with the negative exponent moved and became positive!

14. Negative Exponents - Examples
Remember: You can not have negative or zero exponents in your answer!!
1) Simplify:
Get rid of the negative exponent.
Move to the bottom!
Simplify
Solution

15. Negative Exponents - Examples
Remember: You can not have negative or zero exponents in your answer!!
Get rid of the negative exponent!

16. Here’s a tricky one!

17. Practice
Simplify the following expressions 17

18. Closure
“We learned what?”