1. Lesson 4.5 Rules of Exponents
Essential Question: How do you multiply and divide powers?

2. Before we start… Complete the table. Expression Expanded Expression
Number of Factors
Product as a Power
2 2 ∙ 2 4
2∙2 ∙ 2∙2∙2∙2 6
2 6
3 3 ∙ 3 4
7 2 ∙ 7 1

3. What is a power?
An expression that represents repeated multiplication of the same factor.

4. What are the parts of a power?
A power can be written in a form using two numbers, a base and an exponent.
The exponent represents the number of times the base is used as a factor.

6. Product of Powers Property
Words
To multiply powers with the same base, add their exponents.
Algebra
𝑎 𝑚 ∙ 𝑎 𝑛 = 𝑎 𝑚+𝑛
Numbers
5 6 ∙ 5 3 = = 5 9

7. Find the product. Write your answer using exponents.
2 3 ∙ 2 2

8. Find the product. Write your answer using exponents.
8 7 ∙ 8 8

9. Find the product. Write your answer using exponents.
5∙ 5 6

10. Simplify 𝑥 6 ∙ 𝑥 9

11. Simplify 𝑎 7 ∙ 𝑎 11

12. Simplify 𝑦 7 ∙𝑦

13. Simplify 𝑐 15 ∙ 𝑐 6 ∙𝑐

14. Simplify 𝑥 6 ∙ 𝑦 2 ∙ 𝑥 4

15. Simplify 7 𝑥 2 ∙3 𝑥 3

16. Simplify 𝑠 4 ∙ 𝑠 2

17. Simplify 7𝑥 2 ∙7 𝑥 4

18. Simplify 2𝑛 11 ∙6 𝑛 8

19. Simplify 𝑧∙ 5𝑧 7 ∙ 𝑧 2

20. Quotient of Powers Property
Words
To divide two powers with the same nonzero base, subtract the exponent of the denominator from the exponent of the numerator.
Algebra
𝑎 𝑚 𝑎 𝑛 = 𝑎 𝑚−𝑛
Numbers
= 4 7−4 = 4 3

21. Simplify 𝑥 18 𝑥 9

22. Simplify 𝑎 9 𝑎 2

23. Simplify 𝑤 15 𝑤 4

24. Simplify 𝑑 8 𝑑

25. Simplify 𝑞 3 ∙ 𝑞 5 𝑞 4

26. Simplify 𝑎 2 𝑏 8 𝑏 2

27. Simplify 𝑦 4 ∙𝑦 𝑦 3

28. Simplify 𝑐 𝑐 3

29. Simplify 𝑔 𝑔 2

30. Simplify 3 𝑚 5 ∙ 𝑚 2 6 𝑚 3

31. Simplify 𝑥∙7 𝑥 𝑥 4

32. Simplify 12 𝑦 2 ∙ 𝑦 𝑦 5

33. How do you multiply and divide powers with the same base?
To multiply powers with the same base, add their exponents.
To divide two powers with the same nonzero base, subtract the exponent of the denominator from the exponent of the numerator.

34. How do you multiply and divide expressions with exponents?

35. Ticket Out the Door
Simplify 4 𝑥 3 𝑦 5 ∙6𝑥 𝑦 2 2𝑥𝑦