Section 7.1 Multiplication Properties of Exponents Algebra 1

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

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)

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

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

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 ?

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

Practice Set 1: Product of Powers Ex 1: Simplify 6 𝑛 3 ∙2 𝑛 7 6 𝑛 3 ∙2 𝑛 7 1. 6∙2∙ 𝑛 3 ∙ 𝑛 7 2. 12 𝑛 3+7 3. 12 𝑛 10 Ex 2: Simplify 4 𝑏 2 ∙5 𝑏 7 20 𝑏 9

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

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

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

Problem Set 1: Power of a Power Ex 1) 2 3 4 2 1. 2 3∙4 2 = 2 12 2 2. 2 12∙2 = 2 24 Ex 2) 𝑥 5 2 7 𝑥 70

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 ?

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

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

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 2 10 −2 10 𝑏 40 𝑦 30 𝑎 20

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

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

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

Exit Ticket For Feedback Simplify the following monomial: −2 𝑥 4 𝑦 2 3 𝑥 4 𝑦 2