Lesson 2 NYS COMMON CORE MATHEMATICS CURRICULUM 8•1 Name ___________________________________________ Period _________ Lesson 2.2: Multiplication of Numbers in Exponential Form Classwork In general, if 𝑥 is any number and 𝑚, 𝑛 are positive integers, then 𝑥 𝑚 ∙ 𝑥 𝑛 = 𝑥 𝑚+𝑛 because 𝑥 𝑚 × 𝑥 𝑛 = (𝑥 ⏟ ⋯ 𝑥) × (𝑥 ⏟ ⋯ 𝑥) = (𝑥 ⏟ ⋯ 𝑥) = 𝑥 𝑚+𝑛 𝑚 𝑡𝑖𝑚𝑒𝑠 𝑛 𝑡𝑖𝑚𝑒𝑠 𝑚+𝑛 𝑡𝑖𝑚𝑒𝑠 Simplify the following expressions. Exercise 1 Exercise 5 𝟏𝟒𝟐𝟑 × 𝟏𝟒𝟖 = 𝑎23 ∙ 𝑎8 = Exercise 2 Exercise 6 (−72)10 × (−72)13 = 𝑓 10 ∙ 𝑓 13 = Exercise 3 Exercise 7 𝟓𝟗𝟒 × 𝟓𝟕𝟖 = 𝒃𝟗𝟒 ∙ 𝒃𝟕𝟖 = Exercise 4 Exercise 8 (−𝟑)𝟗 × (−𝟑)𝟓 = Let 𝑥 be a positive integer. If (−3)9 what is 𝑥? Lesson 2: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org (−3)𝑥 = (−3)14 , Multiplication of Numbers in Exponential Form 3/15/16 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. S.5 Lesson 2 NYS COMMON CORE MATHEMATICS CURRICULUM 8•1 What would happen if there were more terms with the same base? Write an equivalent expression for each problem. Exercise 9 Exercise 10 94 × 96 × 913 = 23 × 25 × 27 × 29 = Can the following expressions be simplified? If so, write an equivalent expression. If not, explain why not. Exercise 11 5 9 3 Exercise 14 14 6 ×4 ×4 ×6 24 × 4 × 22 = = Exercise 12 Exercise 15 (−4)2 ∙ 175 ∙ (−4)3 ∙ 177 = 36 × 32 × 35 = Exercise 13 Exercise 16 152 ∙ 72 ∙ 15 ∙ 74 = 54 × 211 = Exercise 17 Simplify the following expression: (2𝑥 3 )(17𝑥 7 ) = Exercise 18 Exercise 19 Use the distributive law to simplify the following expression: Use the distributive law to simplify the following expression: 𝑎(𝑎 + 𝑏) = 𝑏(𝑎 + 𝑏) = Lesson 2: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Multiplication of Numbers in Exponential Form 3/15/16 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. S.6