Module 1-­‐Lesson 1: Exponential Notation Classwork/Notes 𝟗 𝟒
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𝟓𝟔 means 𝟓×𝟓×𝟓×𝟓×𝟓×𝟓 and ! ! means × × × . You have seen this kind of notation before, it is called exponential notation. In general, for any number 𝒙 and any positive integer 𝒏, 𝒙𝒏 = (𝒙
∙ 𝒙 ⋯!!
𝒙) !!!!!
𝒏 𝒕𝒊𝒎𝒆𝒔
𝒏
The number 𝒙 is called 𝒙 raised to the 𝒏-­‐th power, 𝒏 is the exponent of 𝒙 in 𝒙𝒏 and 𝒙 is the base of 𝒙𝒏 . Exercise 1 Exercise 2 3.6× ⋯×3.6 = 3.6!" 4× ⋯×4 = Exercise 3 ! !"#$%
−11.63)× ⋯×(−11.63 = _______ !"#$%
Exercise 4 Exercise 5 12× ⋯×12 = 12!" −5 × ⋯× −5 = _______!"#$%
!" !"#$%
Exercise 7 −
! !"#$%
1
1
× ⋯× −
= 14
14
Exercise 10 Exercise 6 7
7
× ⋯× = 2
2
!" !"#$%
Exercise 8 −13 × ⋯× −13 = !" !"#$%
!" !"#$%
Exercise 9 𝑥 ∙ 𝑥 ⋯ 𝑥 = !"# !"#$%
𝑥 ∙ 𝑥 ⋯ 𝑥 = 𝑥 ! _______!"#$%
Exercise 11 Will these products be positive or negative? How do you know? −1 × −1 × ⋯× −1 = −1
!" !"#$%
!"
−1 × −1 × ⋯× −1 = −1
!" !"#$%
!"
Exercise 12 Is it necessary to do all of the calculations to determine the sign of the product? Why or why not? −5 × −5 × ⋯× −5 = −5
!" !"#$%
!"
−1.8 × −1.8 × ⋯× −1.8 = −1.8
!"" !"#$%
!""
Exercise 13 Fill in the blanks about whether the number is positive or negative. If 𝑛 is a positive even number, then −55 ! is __________________________. If 𝑛 is a positive odd number, then −72.4 ! is __________________________. Exercise 14 Josie says that −15 × ⋯× −15 = −15! . Is she correct? How do you know? ! !"#$%
Exercise 15 Rewrite each number in exponential notation using 3 as the base. a. 3 = ______ b. 9 = ______ c. 27 = _______ d. 81 = _______ e. 243 = _______ f. 729 = ________ Exercise 16 Write 45 and 43 as products of factors in order to predict the answer to 45 ∙ 43. Write your answer using a single exponent and base of 4. Exercise 17 !!
Write 27 and 23 as products of factors in order to predict the answer to ! . Write your answer using a single exponent and base of 2. !