1. 8.5
Dividing Exponents

2. 8.5 – Dividing Exponents Warm Up Simplify. 1. (x2)3 3. 5. 2. 4. 6.
Write in Scientific Notation. 7. 8.

3. 8.5 – Dividing Exponents Objective
Use division properties of exponents to evaluate and simplify expressions.

4. 8.5 – Dividing Exponents
A quotient of powers with the same base can be found by writing the powers in a factored form and dividing out common factors.
Notice the relationship between the exponents in the original quotient and the exponent in the final answer: 5 – 3 = 2.

5. 8.5 – Dividing Exponents

6. 8.5 – Dividing Exponents
When we multiply exponents with the same base ADD the exponents!
When we divide exponents with the same base SUBTRACT the exponents!!! 5 4 5 4
4 + 4 5 8 = 5 = * 5 6 2 5
6 - 2 5 4 = =

7. Example 1: Finding Quotients of Powers
8.5 – Dividing Exponents
Example 1: Finding Quotients of Powers
Simplify. A. B.

8. Example 1: Finding Quotients of Powers
8.5 – Dividing Exponents
Example 1: Finding Quotients of Powers
Simplify. C. D.

9. 8.5 – Dividing Exponents
Check It Out! Example 1
Simplify. a. b.

10. 8.5 – Dividing Exponents
Check It Out! Example 1
Simplify. c. d.

11. 8.5 – Dividing Exponents
Simplify: 6 a 14 a

12. 8.5 – Dividing Exponents
Simplify: -1 3
c d 5
- 4
c d

13. 8.5 – Dividing Exponents
Simplify: 4 b 9 b

14. 8.5 – Dividing Exponents
Simplify: 10 z 5 z

15. Example 2: Dividing Numbers in Scientific Notation
8.5 – Dividing Exponents
Example 2: Dividing Numbers in Scientific Notation
Simplify and write the answer in scientific notation
Write as a product of quotients.
Simplify each quotient.
Simplify the exponent.
Write 0.5 in scientific notation as 5 x
The second two terms have the same base, so add the exponents.
Simplify the exponent.

16. 8.5 – Dividing Exponents Example 3: Application
The Michigan Department of Education spent about dollars in fiscal year on public schools. There were about students enrolled in public school. What was the average spending per student? Write your answer in standard form.
To find the average spending per student, divide the total debt by the number of students.
Write as a product of quotients.

17. 8.5 – Dividing Exponents Example 3 Continued
The Michigan Department of Education spent about dollars in fiscal year on public schools. There were about students enrolled in public school. What was the average spending per student? Write your answer in standard form.
To find the average spending per student, divide the total debt by the number of students.
Simplify each quotient.
Simplify the exponent.
Write in standard form.
The average spending per student is $5,800.

18. ( ) 8.5 – Dividing Exponents
What happens if we have an expression like this? ( ) 3 4 2 x

19. 8.5 – Dividing Exponents
A power of a quotient can be found by first writing the numerator and denominator as powers.
Notice that the exponents in the final answer are the same as the exponent in the original expression.

20. 8.5 – Dividing Exponents

21. Example 4A: Finding Positive Powers of Quotient
8.5 – Dividing Exponents
Example 4A: Finding Positive Powers of Quotient
Simplify.
Use the Power of a Quotient Property.
Simplify.

22. Example 4B: Finding Positive Powers of Quotient
8.5 – Dividing Exponents
Example 4B: Finding Positive Powers of Quotient
Simplify.
Use the Power of a Product Property.
Use the Power of a Product Property:
Simplify and use the Power of a Power Property:

23. Example 4C: Finding Positive Powers of Quotient
8.5 – Dividing Exponents
Example 4C: Finding Positive Powers of Quotient
Simplify.
Use the Power of a Product Property.
Use the Power of a Product Property:
Use the Power of a Product Property:

24. 8.5 – Dividing Exponents Example 4C Continued Simplify.
Use the Power of a Product Property:

25. 8.5 – Dividing Exponents Check It Out! Example 4a Simplify.
Use the Power of a Quotient Property.
Simplify.

26. 8.5 – Dividing Exponents
Check It Out! Example 4b
Simplify.

27. 8.5 – Dividing Exponents
Check It Out! Example 4c
Simplify.

28. 8.5 – Dividing Exponents
Simplify ( ) 2 3 2 x

29. 8.5 – Dividing Exponents
Simplify ( ) 3 x 2 y

30. 8.5 – Dividing Exponents
Simplify ( )
- 2 3 5

31. Example 5A: Finding Negative Powers of Quotients
8.5 – Dividing Exponents
Example 5A: Finding Negative Powers of Quotients
Simplify.
Rewrite with a positive exponent.
Use the Powers of a Quotient Property .
and

32. Example 5B: Finding Negative Powers of Quotients
8.5 – Dividing Exponents
Example 5B: Finding Negative Powers of Quotients
Simplify.

33. 8.5 – Dividing Exponents 1. 5.
Lesson Quiz: Part I
Simplify. 2.