Notes and Homework Link

Lesson 1
NYS COMMON CORE MATHEMATICS CURRICULUM
8β€’1
Lesson 1: Exponential Notation
Classwork
πŸ— πŸ’
πŸ“πŸ” means πŸ“ × πŸ“ × πŸ“ × πŸ“ × πŸ“ × πŸ“ and (πŸ•) means
πŸ—
πŸ•
×
πŸ—
πŸ•
×
πŸ—
πŸ•
πŸ—
× .
πŸ•
You have seen this kind of notation before, it is called exponential notation. In general, for any number 𝒙 and any
positive integer 𝒏,
(𝒙 βˆ™ 𝒙 β‹― 𝒙)
𝒙𝒏 = ⏟
𝒏 π’•π’Šπ’Žπ’†π’”
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 6
4×β‹―×4 =
⏟
7
7
×β‹―× =
⏟
2
2
7 π‘‘π‘–π‘šπ‘’π‘ 
21 π‘‘π‘–π‘šπ‘’π‘ 
Exercise 2
Exercise 7
3.6 × β‹― × 3.6 = 3.647
⏟
(βˆ’13) × β‹― × (βˆ’13) =
⏟
_______ π‘‘π‘–π‘šπ‘’π‘ 
6 π‘‘π‘–π‘šπ‘’π‘ 
Exercise 3
Exercise 8
(βˆ’11.63)
× β‹― × (βˆ’11.63) =
⏟
1
1
(βˆ’ ) × β‹― × (βˆ’ ) =
⏟ 14
14
34 π‘‘π‘–π‘šπ‘’π‘ 
10 π‘‘π‘–π‘šπ‘’π‘ 
Exercise 4
Exercise 9
12 × β‹― × 12 = 1215
⏟
π‘₯ βˆ™ π‘₯ β‹―π‘₯ =
⏟
185 π‘‘π‘–π‘šπ‘’π‘ 
_______π‘‘π‘–π‘šπ‘’π‘ 
Exercise 5
Exercise 10
π‘₯ βˆ™ π‘₯ β‹― π‘₯ = π‘₯𝑛
⏟
(βˆ’5)
⏟ × β‹― × (βˆ’5) =
_______π‘‘π‘–π‘šπ‘’π‘ 
10 π‘‘π‘–π‘šπ‘’π‘ 
Lesson 1:
Date:
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
Exponential Notation
1/4/17
S.1
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Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 1
8β€’1
Exercise 11
Will these products be positive or negative? How do you know?
(βˆ’1)
⏟ × (βˆ’1) × β‹― × (βˆ’1) = (βˆ’1)12
12 π‘‘π‘–π‘šπ‘’π‘ 
(βˆ’1) × (βˆ’1) × β‹― × (βˆ’1) = (βˆ’1)13
⏟
13 π‘‘π‘–π‘šπ‘’π‘ 
Exercise 12
Is it necessary to do all of the calculations to determine the sign of the product? Why or why not?
(βˆ’5) × (βˆ’5) × β‹― × (βˆ’5) = (βˆ’5)95
⏟
95 π‘‘π‘–π‘šπ‘’π‘ 
(βˆ’1.8)
× (βˆ’1.8) × β‹― × (βˆ’1.8) = (βˆ’1.8)122
⏟
122 π‘‘π‘–π‘šπ‘’π‘ 
Lesson 1:
Date:
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
Exponential Notation
1/4/17
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Lesson 1
NYS COMMON CORE MATHEMATICS CURRICULUM
8β€’1
Exercise 13
Fill in the blanks about whether the number is positive or negative.
If 𝑛 is a positive even number, then (βˆ’55)𝑛 is __________________________.
If 𝑛 is a positive odd number, then (βˆ’72.4)𝑛 is __________________________.
Exercise 14
(βˆ’15) × β‹― × (βˆ’15) = βˆ’156 . Is she correct? How do you know?
Josie says that ⏟
6 π‘‘π‘–π‘šπ‘’π‘ 
Lesson 1:
Date:
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
Exponential Notation
1/4/17
S.3
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Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 1
NYS COMMON CORE MATHEMATICS CURRICULUM
8β€’1
Problem Set
1.
Use what you know about exponential notation to complete the expressions below.
(βˆ’πŸ“) × β‹― × (βˆ’πŸ“) =
⏟
πŸ‘. πŸ• × β‹― × πŸ‘. πŸ• = πŸ‘. πŸ•πŸπŸ—
⏟
_____ π’•π’Šπ’Žπ’†π’”
πŸπŸ• π’•π’Šπ’Žπ’†π’”
πŸ• × β‹― × πŸ• = πŸ•πŸ’πŸ“
⏟
πŸ”×β‹―×πŸ” =
⏟
πŸ’ π’•π’Šπ’Žπ’†π’”
_____ π’•π’Šπ’Žπ’†π’”
(βˆ’πŸ. 𝟏) × β‹― × (βˆ’πŸ. 𝟏) =
⏟
πŸ’. πŸ‘ × β‹― × πŸ’. πŸ‘ =
⏟
πŸπŸ‘ π’•π’Šπ’Žπ’†π’”
πŸ— π’•π’Šπ’Žπ’†π’”
𝟏𝟏
𝟏𝟏
𝟏𝟏 𝒙
(βˆ’ ) × β‹― × (βˆ’ ) = (βˆ’ )
⏟ πŸ“
πŸ“
πŸ“
𝟐
𝟐
( )×β‹―×( ) =
βŸπŸ‘
πŸ‘
πŸπŸ— π’•π’Šπ’Žπ’†π’”
_____ π’•π’Šπ’Žπ’†π’”
(βˆ’πŸπŸ) × β‹― × (βˆ’πŸπŸ) = (βˆ’πŸπŸ)πŸπŸ“
⏟
𝒂×β‹―×𝒂 =
⏟
π’Ž π’•π’Šπ’Žπ’†π’”
_____ π’•π’Šπ’Žπ’†π’”
2.
Write an expression with (βˆ’1) as its base that will produce a positive product.
3.
Write an expression with (βˆ’1) as its base that will produce a negative product.
4.
Tim wrote 16 as (βˆ’2)4 . Is he correct?
5.
Could βˆ’2 be used as a base to rewrite 32? 64? Why or why not?
Lesson 1:
Date:
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
Exponential Notation
1/4/17
S.4
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.