The document discusses exponents and scientific notation. It defines exponential form as representing multiplying a number by itself numerous times, with the base as the number being multiplied and the exponent as the number of times. It provides examples of evaluating expressions using exponent rules like the power, product, and quotient rules. It also demonstrates writing numbers in scientific notation and evaluating expressions for given variable values.
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Integrated Math 2 Sections 2-7 and 2-8
1. SECTIONS 2-7 AND 2-8
Properties of Exponents and Zero and Negative
Exponents
2. ESSENTIAL QUESTIONS
How do you choose appropriate units of measure?
How do you evaluate variable expressions?
How do you write numbers using zero and negative integers as
exponents?
How do you write numbers in scientific notation?
Where you’ll see this:
Biology, finance, computers, population, physics, astronomy
4. VOCABULARY
1. Exponential Form: The form you use to represent
multiplying a number by itself numerous times
2. Base:
3. Exponent:
4. Standard Form:
5. Scientific Notation:
5. VOCABULARY
1. Exponential Form: The form you use to represent
multiplying a number by itself numerous times
2. Base: The number that is being multiplied over and
over
3. Exponent:
4. Standard Form:
5. Scientific Notation:
6. VOCABULARY
1. Exponential Form: The form you use to represent
multiplying a number by itself numerous times
2. Base: The number that is being multiplied over and
over
3. Exponent: The number of times we multiply the base
4. Standard Form:
5. Scientific Notation:
7. VOCABULARY
1. Exponential Form: The form you use to represent
multiplying a number by itself numerous times
2. Base: The number that is being multiplied over and
over
3. Exponent: The number of times we multiply the base
4. Standard Form: Any number in decimal form
5. Scientific Notation:
8. VOCABULARY
1. Exponential Form: The form you use to represent
multiplying a number by itself numerous times
2. Base: The number that is being multiplied over and
over
3. Exponent: The number of times we multiply the base
4. Standard Form: Any number in decimal form
5. Scientific Notation: A number with two factors, where
the first factor is a number ≥ 1 and < 10, and the
second is a power of 10.
9. ACTIVITY: PAGE 82
Hours 1 2 3 4 5
# of
2 4 8 16 32
organisms
Pattern:
Sixth hour: Seventh hour: Eighth hour:
How long until there are 2000?
10. ACTIVITY: PAGE 82
Hours 1 2 3 4 5
# of
2 4 8 16 32
organisms
Pattern:
Sixth hour: Seventh hour: Eighth hour:
How long until there are 2000?
11. ACTIVITY: PAGE 82
Hours 1 2 3 4 5
# of
2 4 8 16 32
organisms
Pattern:
Sixth hour: Seventh hour: Eighth hour:
How long until there are 2000?
12. ACTIVITY: PAGE 82
Hours 1 2 3 4 5
# of
2 4 8 16 32
organisms
Pattern:
Sixth hour: Seventh hour: Eighth hour:
How long until there are 2000?
13. ACTIVITY: PAGE 82
Hours 1 2 3 4 5
# of
2 4 8 16 32
organisms
Pattern:
Sixth hour: Seventh hour: Eighth hour:
How long until there are 2000?
14. ACTIVITY: PAGE 82
Hours 1 2 3 4 5
# of
2 4 8 16 32
organisms
Pattern:
Sixth hour: Seventh hour: Eighth hour:
How long until there are 2000?
15. ACTIVITY: PAGE 82
Hours 1 2 3 4 5
# of
2 4 8 16 32
organisms
Pattern: The number of organisms doubles
Sixth hour: Seventh hour: Eighth hour:
How long until there are 2000?
16. ACTIVITY: PAGE 82
Hours 1 2 3 4 5
# of
2 4 8 16 32
organisms
Pattern: The number of organisms doubles
Sixth hour: 64 Seventh hour: Eighth hour:
How long until there are 2000?
17. ACTIVITY: PAGE 82
Hours 1 2 3 4 5
# of
2 4 8 16 32
organisms
Pattern: The number of organisms doubles
Sixth hour: 64 Seventh hour: 128 Eighth hour:
How long until there are 2000?
18. ACTIVITY: PAGE 82
Hours 1 2 3 4 5
# of
2 4 8 16 32
organisms
Pattern: The number of organisms doubles
Sixth hour: 64 Seventh hour: 128 Eighth hour: 256
How long until there are 2000?
19. ACTIVITY: PAGE 82
Hours 1 2 3 4 5
# of
2 4 8 16 32
organisms
Pattern: The number of organisms doubles
Sixth hour: 64 Seventh hour: 128 Eighth hour: 256
How long until there are 2000? 11th hour
20. EXAMPLE 1
Evaluate for x = .8 and y = 1.2.
2 3 2
a. 3x y b. (4x) y
21. EXAMPLE 1
Evaluate for x = .8 and y = 1.2.
2 3 2
a. 3x y b. (4x) y
= 3(.8) (1.2)
2
22. EXAMPLE 1
Evaluate for x = .8 and y = 1.2.
2 3 2
a. 3x y b. (4x) y
= 3(.8) (1.2)
2
= 3(.64)(1.2)
23. EXAMPLE 1
Evaluate for x = .8 and y = 1.2.
2 3 2
a. 3x y b. (4x) y
= 3(.8) (1.2)
2
= 3(.64)(1.2)
= 2.304
24. EXAMPLE 1
Evaluate for x = .8 and y = 1.2.
2 3 2
a. 3x y b. (4x) y
= 3(.8) (1.2)
2
= [4(.8)] (1.2)
3 2
= 3(.64)(1.2)
= 2.304
25. EXAMPLE 1
Evaluate for x = .8 and y = 1.2.
2 3 2
a. 3x y b. (4x) y
= 3(.8) (1.2)
2
= [4(.8)] (1.2)
3 2
= 3(.64)(1.2) = (3.2) (1.2)
3 2
= 2.304
26. EXAMPLE 1
Evaluate for x = .8 and y = 1.2.
2 3 2
a. 3x y b. (4x) y
= 3(.8) (1.2)
2
= [4(.8)] (1.2)
3 2
= 3(.64)(1.2) = (3.2) (1.2)
3 2
= 2.304 = (32.768)(1.44)
27. EXAMPLE 1
Evaluate for x = .8 and y = 1.2.
2 3 2
a. 3x y b. (4x) y
= 3(.8) (1.2)
2
= [4(.8)] (1.2)
3 2
= 3(.64)(1.2) = (3.2) (1.2)
3 2
= 2.304 = (32.768)(1.44)
= 47.18592
79. PROPERTY OF NEGATIVE
EXPONENTS
1
b −m
= m
b
3
h −4
7 = h =h
3−7
h
3
h hihih
7
=
h hihihihihihih
80. PROPERTY OF NEGATIVE
EXPONENTS
1
b −m
= m
b
3
h −4
7 = h =h
3−7
h
3
h hihih 1
7
= = 4
h hihihihihihih h
81. EXAMPLE 4
Simplify each expression. Write the answer with a
positive exponent.
2
x 1
a. 8 3
b. y i 4 −3 2
x c. (z )
y
82. EXAMPLE 4
Simplify each expression. Write the answer with a
positive exponent.
2
x 1
a. 8 3
b. y i 4 −3 2
x c. (z )
y
=x 2− 8
83. EXAMPLE 4
Simplify each expression. Write the answer with a
positive exponent.
2
x 1
a. 8 3
b. y i 4 −3 2
x c. (z )
y
=x 2− 8
−6
=x
84. EXAMPLE 4
Simplify each expression. Write the answer with a
positive exponent.
2
x 1
a. 8 3
b. y i 4 −3 2
x c. (z )
y
=x 2− 8
−6
=x
1
= 6
x
85. EXAMPLE 4
Simplify each expression. Write the answer with a
positive exponent.
2
x 1
a. 8 3
b. y i 4 −3 2
x c. (z )
y
3
y
=x 2− 8
= 4
y
−6
=x
1
= 6
x
86. EXAMPLE 4
Simplify each expression. Write the answer with a
positive exponent.
2
x 1
a. 8 3
b. y i 4 −3 2
x c. (z )
y
3
y
=x 2− 8
= 4
y
−6
=x =y −1
1
= 6
x
87. EXAMPLE 4
Simplify each expression. Write the answer with a
positive exponent.
2
x 1
a. 8 3
b. y i 4 −3 2
x c. (z )
y
3
y
=x 2− 8
= 4
y
−6
=x =y −1
1 1
= 6 =
x y
88. EXAMPLE 4
Simplify each expression. Write the answer with a
positive exponent.
2
x 1
a. 8 3
b. y i 4 −3 2
x c. (z )
y
3
−6
=x 2− 8
= 4
y =z
y
−6
=x =y −1
1 1
= 6 =
x y
89. EXAMPLE 4
Simplify each expression. Write the answer with a
positive exponent.
2
x 1
a. 8 3
b. y i 4 −3 2
x c. (z )
y
3
−6
=x 2− 8
= 4
y =z
y
=x −6 1
=y −1
= 6
1 1 z
= 6 =
x y
90. EXAMPLE 5
Evaluate each expression when m = -2 and n = 4.
4 3 −2 5 −3
a. 6m b. (n ) c. m n
91. EXAMPLE 5
Evaluate each expression when m = -2 and n = 4.
4 3 −2 5 −3
a. 6m b. (n ) c. m n
= 6(−2) 4
92. EXAMPLE 5
Evaluate each expression when m = -2 and n = 4.
4 3 −2 5 −3
a. 6m b. (n ) c. m n
= 6(−2) 4
= 6(16)
93. EXAMPLE 5
Evaluate each expression when m = -2 and n = 4.
4 3 −2 5 −3
a. 6m b. (n ) c. m n
= 6(−2) 4
= 6(16)
= 96
94. EXAMPLE 5
Evaluate each expression when m = -2 and n = 4.
4 3 −2 5 −3
a. 6m b. (n ) c. m n
−6
= 6(−2) 4
=n
= 6(16)
= 96
95. EXAMPLE 5
Evaluate each expression when m = -2 and n = 4.
4 3 −2 5 −3
a. 6m b. (n ) c. m n
−6
= 6(−2) 4
=n
= 6(16) 1
= 6
n
= 96
96. EXAMPLE 5
Evaluate each expression when m = -2 and n = 4.
4 3 −2 5 −3
a. 6m b. (n ) c. m n
−6
= 6(−2) 4
=n
= 6(16) 1
= 6
n
= 96
1
= 6
4
97. EXAMPLE 5
Evaluate each expression when m = -2 and n = 4.
4 3 −2 5 −3
a. 6m b. (n ) c. m n
−6
= 6(−2) 4
=n
= 6(16) 1
= 6
n
= 96
1 1
= 6 =
4 4096
98. EXAMPLE 5
Evaluate each expression when m = -2 and n = 4.
4 3 −2 5 −3
a. 6m b. (n ) c. m n
−6 −3
= 6(−2) 4
=n = (−2) (4)
5
= 6(16) 1
= 6
n
= 96
1 1
= 6 =
4 4096
99. EXAMPLE 5
Evaluate each expression when m = -2 and n = 4.
4 3 −2 5 −3
a. 6m b. (n ) c. m n
−6 −3
= 6(−2) 4
=n = (−2) (4)
5
= 6(16) 1 (−2) 5
= 6 = 3
n (4)
= 96
1 1
= 6 =
4 4096
100. EXAMPLE 5
Evaluate each expression when m = -2 and n = 4.
4 3 −2 5 −3
a. 6m b. (n ) c. m n
−6 −3
= 6(−2) 4
=n = (−2) (4)
5
= 6(16) 1 (−2) 5
= 6 = 3
n (4)
= 96
1 1 −32
= 6 = =
4 4096 64
101. EXAMPLE 5
Evaluate each expression when m = -2 and n = 4.
4 3 −2 5 −3
a. 6m b. (n ) c. m n
−6 −3
= 6(−2) 4
=n = (−2) (4)
5
= 6(16) 1 (−2) 5
= 6 = 3
n (4)
= 96
1 1 −32 −1
= 6 = = =
4 4096 64 2
102. EXAMPLE 6
Write in scientific notation.
a. .0000013 b. 230,000,000,000
103. EXAMPLE 6
Write in scientific notation.
a. .0000013 b. 230,000,000,000
-6
=1.3i10
104. EXAMPLE 6
Write in scientific notation.
a. .0000013 b. 230,000,000,000
-6 11
=1.3i10 =2.3i10
105. EXAMPLE 7
Write in standard form.
6 −9
a. 7.2i10 b. 3.5i10
106. EXAMPLE 7
Write in standard form.
6 −9
a. 7.2i10 b. 3.5i10
= 7, 200,000
107. EXAMPLE 7
Write in standard form.
6 −9
a. 7.2i10 b. 3.5i10
= 7, 200,000 = .0000000035
108. EXAMPLE 8
−24
The mass of one hydrogen atom is 1.67i10
grams. Find the mass of 2,700,000,000,000,000
hydrogen atoms.
109. EXAMPLE 8
−24
The mass of one hydrogen atom is 1.67i10
grams. Find the mass of 2,700,000,000,000,000
hydrogen atoms.
−24 15
(1.67i10 )(2.7i10 )
110. EXAMPLE 8
−24
The mass of one hydrogen atom is 1.67i10
grams. Find the mass of 2,700,000,000,000,000
hydrogen atoms.
−24 15
(1.67i10 )(2.7i10 )
−24
= (1.67i2.7)(10 i10 15
)
111. EXAMPLE 8
−24
The mass of one hydrogen atom is 1.67i10
grams. Find the mass of 2,700,000,000,000,000
hydrogen atoms.
−24 15
(1.67i10 )(2.7i10 )
−24
= (1.67i2.7)(10 i10 15
)
−9
= 4.509i10
112. EXAMPLE 8
−24
The mass of one hydrogen atom is 1.67i10
grams. Find the mass of 2,700,000,000,000,000
hydrogen atoms.
−24 15
(1.67i10 )(2.7i10 )
−24
= (1.67i2.7)(10 i10 15
)
−9
= 4.509i10
= .000000004509 gram
114. HOMEWORK
p. 84 #1-48 multiples of 3; p. 88 #1-48 multiples of 3
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