Lesson 2
NYS COMMON CORE MATHEMATICS CURRICULUM
8•1
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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