1. Section 7.1 Multiplication Properties of Exponents
Algebra 1

2. Learning Targets Define the terms monomial and constant
Identify monomial and constant expressions
Define & apply the product of powers property
Define & apply the power of a power property
Define and apply the power of a product property
Simplify monomial expressions

3. Monomial
Monomial: an expression with one term Ex 1) 10 Ex 3) 3 𝑥 2 𝑦 Ex 2) x Ex 4) 2𝑧 𝑦 Key Point: only contains multiplication or division (doesn’t contain addition or subtraction)

4. Constant
Constant: a monomial that has only real numbers (no variables) Ex 1) 4 Ex 3) -6 Ex 2) 10 Ex 4) 2 5

5. Practice: Identification
Identify which of the following are monomials
Of the monomials, which are constants?
− 7 9
𝑚𝑝 𝑟
𝑓+24
−𝑥+5
𝑗 2 +16
𝑥𝑦 𝑧 2 2
ℎ 2
23𝑎𝑏 𝑐 2 15
− 𝑥 2 +4𝑥+6

6. Recall: Exponent Definition
Exponent/Power
3 4
Base
=3∙3∙3∙3=81

7. Exploration: Talk with your groups
1. Find the missing exponent: 2 3 ∙ 2 4 = 2 ? 2. Find the missing exponent: 𝑥 2 ∙ 𝑥 5 = 𝑥 ? Can you find a shortcut? Test your shortcut on the following 𝑦 7 ∙ 𝑦 2 = 𝑦 ?

8. Product of Powers
𝑎 𝑚 ∙ 𝑎 𝑛 = 𝑎 𝑚+𝑛 Example) 𝑏 3 ∙ 𝑏 5 = 𝑏 3+5 = 𝑏 8

9. Practice Set 1: Product of Powers
Ex 1: Simplify 6 𝑛 3 ∙2 𝑛 7 6 𝑛 3 ∙2 𝑛 ∙2∙ 𝑛 3 ∙ 𝑛 𝑛 𝑛 10
Ex 2: Simplify 4 𝑏 2 ∙5 𝑏 7
20 𝑏 9

10. Problem Set 2: Product of Powers
Ex 1: Simplify 3𝑝 𝑡 3 ∙− 𝑝 3 𝑡 4 3𝑝 𝑡 3 ∙− 𝑝 3 𝑡 ∙−1∙𝑝∙ 𝑝 3 ∙ 𝑡 3 ∙ 𝑡 4 2. −3 𝑝 1+3 𝑡 −3 𝑝 4 𝑡 7
Ex 2:
Simplify −4 𝑧 2 𝑦∙− 𝑧 4 𝑦 3
4 𝑧 6 𝑦 4

11. Exploration: Talk with your groups
1. Find the exponent: = 3 ? 2. Find the exponent: 𝑟 4 3 = 𝑟 ? Can you find a shortcut? Test your shortcut on the following 𝑦 8 3 = 𝑦 ?

12. Power of a Power Property
𝑎 𝑚 𝑛 = 𝑎 𝑚∙𝑛 Example) 𝑥 4 5 = 𝑥 4∙5 = 𝑥 20

13. Problem Set 1: Power of a Power
Ex 1) ∙4 2 = ∙2 = 2 24
Ex 2) 𝑥
𝑥 70

14. Exploration: Talk with your groups
1. Find the missing exponents: 𝑡𝑤 3 = 𝑡 ? 𝑤 ? 2. Find the missing exponents: 2𝑦 4 = 2 ? 𝑦 ? Can you find a shortcut? Test your shortcut on the following problem 𝑥𝑦 7 = 𝑥 ? 𝑦 ?

15. Power of a Product Property
𝑎𝑏 𝑚 = 𝑎 𝑚 𝑏 𝑚 Example) −2𝑥 𝑦 3 5 = −2 5 𝑥 5 𝑦 15

16. Practice Set 1: Power of a Product
Ex 1: 2𝑥 𝑦 𝑥 2 𝑦 2∙ 𝑥 2 𝑦 4
Ex 2: −3 𝑥 2 𝑦 4 3
−3 3 𝑥 6 𝑦 12
−27 𝑥 6 𝑦 12

17. Practice Set 2: Power of a Product
Ex 1: 𝑧 2 𝑦 4 𝑥 5 1. 𝑧 2∙5 𝑦 4∙5 𝑥 5 2. 𝑧 10 𝑦 20 𝑥 5
Ex 2: −2 𝑏 4 𝑦 3 𝑎
− 𝑏 40 𝑦 30 𝑎 20

18. Putting it All Together: Simplifying Monomial Expressions
2∙ 9 5 𝑞 22

19. Putting it All Together: Simplifying Monomial Expressions
1. −7 3 𝑎 3 𝑏 12 𝑐 3 𝑎 6 𝑐 6
2. −7 3 𝑎 9 𝑏 12 𝑐 9

20. Worksheet Chart Fill out the chart on your worksheet
Write the definitions, an example, and key characteristics to help you organize the differences between the properties

21. Exit Ticket For Feedback
Simplify the following monomial: −2 𝑥 4 𝑦 𝑥 4 𝑦 2