Properties Of Exponents
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Transcript of Properties Of Exponents
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Properties of Exponents
p. 323
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Properties of Exponentsa&b are real numbers, m&n are integers
• Product Property:• Quotient of Powers:
• Power of a Power Property: • Power of a Product Property:
• Negative Exponent Property:• Zero Exponent Property: • Power of Quotient:
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Example – Product Property
• (-5) 3 (-5) 2 = • (-5)(-5)(-5)(-5)(-5)=• (-5) 5
• (-5)3+2 =• (-5) 5
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Example – Product Property
• x5 • x2 = x•x•x•x•x•x•x
• x5+2 =
• x7
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Product Property a&b are real numbers, m&n are integers
• Product Property: (am )(an)=am+n
• a3• a5 • a4 =
• a3• a5 • a4 = a3+5+4
• a3• a5 • a4 = a12
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Product Property
• (a3 b2) (a4 b6) = • (a3 a4) (b2 b6) = a3+4 b2+6
• a3+4 b2+6 = a7 b8
• (x5 y2) (x4 y7) = • (x5 x4) (y2 y7) = x5+4 y2+7
• x5+2 y2+7 = x9 y9
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You try
• (3x6 y4) (4xy7) =
• (3x6 y4) (4xy7) = (3•4)x6+1 • y4+7
• (3•4)x6+1 • y4+7 = 12x7y11
• (2x12 y5) (6x3 y9) =
• (2• 6)x12+3 y5+9 =12x15y14
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Do now
• (2x4 y4) (5xy7) =
• (2x4 y4) (5xy7) = (2•5)x4+1 • y4+7
• (2•5)x4+1 • y4+7 = 10x5y11
• (3x14 y5) (9x3 y) =
• (3• 9)x14+3 y5+1 =27x17y6
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Dividing Powers with Like bases
• -5 3 = -5• -5• -5-5 2 -5• -5
• -5• -5• -5 = -5
-5• -5
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Power of a Quotient with like bases
• x 4 = x• x • x• x
X2 x• x
• X2
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Quotient of Powers
3
5
x
x 35x 2x
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Quotient of Powers
• Quotient of Powers:
• am = am-n; a≠0
an
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You try
• 45x4y7 = 43x2y6
• 45x4y7 = 45-3 x4-2y7-6
43x2y6
• 45-3 x4-2y7-6 = 42x2y = 16x2y
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You try
• 37x9y12 = 34x5y6
• 37x9y12 = 37-4 x9-5 y12-6
34x5y6
• 37-4 x9-5 y12-6= 33x4y8 = 27x4y8
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Negative Exponents
• x 2 = x• x_____ x4 x• x • x• x• 1 = x2
• x 2 = x 2 -4 = x-2
X4
x-2 = 1
x2
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Negative exponets
• x 3 = x• x_ • x___ x5 x• x • x• x • x• 1 = x3
• x 3 = x 3 -5 = x-3
x5
• x-3 = 1 x3
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Example – Quotient of Powers
10
5
x
x 105x 5x 5
1
x
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You try
• x-2 =• 1 x2
2x-2y = 2x-2y = 2y x2
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You try
• (-5)-6(-5)4 =
• (-5)-6+4 =
• (-5)-2 =
25
1
25
1
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Properties of Exponentsa&b are real numbers, m&n are integers
• Negative Exponent Property:
• a-m= ; a≠0ma
1
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Zero Exponent Property
• x0
• x2 = x2-2
x2
x2-2 = x0
• x2 = 1
x2
x0= 1
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You try
(x-2) (x2) =
(x-2) (x2) = x-2+2
x-2+2 = x0
x0 = 1
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Properties of Exponentsa&b are real numbers, m&n are integers ets Review
• Zero Exponent Property: a0=1; a≠0
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Properties of Exponentsa&b are real numbers, m&n are integers
• Product Property: am * an=am+n
• Quotient of Powers: am = am-n; a≠0 an
• Negative Exponent Property: a-m= ; a≠0
• Zero Exponent Property: a0=1; a≠0
ma
1
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Journal Entry:Describe the rules for the follwoing
• Product Property: • Quotient of Powers:
• Negative Exponent Property:• Zero Exponent Property:
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Example – Power of a Power
• (23)4 = (23) (23) (23) (23)4
• 23+3+3+3 =
• (23)4 = 212
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Example - Power of a Power
• (34)3 = (34) (34) (34)
• (34) (34) (34) = 34+4+4
• (34)3 = 312
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Raising a Power to a Power
•(X5)2 = (X5) (X5)
•(X5) (X5)= x5+5
•(X5)2 = x10
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Power of a Power Property a&b are real numbers, m&n are integers
• Power of a Power Property: (am)n=amn
• (x5)3 = x5•3
• x5•3= x15
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You try
• (y4)8 =
• (y4)8 = y4•8 = y24
• (s3)4 =
• (s3)4 = s3•4 = s12
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Power of a Product Property
• (-2x7)2 = (-2x7) (-2x7)
• (-2x7) (-2x7) = (-2• -2) (x7 •x7) =4x14
• (-2x7)2 = (-2)2 (x7)2 = -21•2 x7•2
• = 4x14
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• Power of a Product Property: (ab)m=ambm
• (a3b2)4= (a3)4 (b2)4
• (a3)4 (b2)4 = a3•4b2•4 =a12b8
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You try
• (-2x4)3 = (-2)1•3 x5•3
• (-2x4)3 = (-2)1•3 x4•3
• (-2)1•3 x4•3 = (-2)3 x12 = -16x12
• (4x4y5)2
• (4x4y5)2 = 41•2x4 •2y5•2
• (4x4y5)2 = 16x8y10
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You try
• (-3x5y3)4 =
• (-3)1•4 x5•4 y4•4= (-3)4 x20 y16
• (7x3y-5)2
• 71•2x3 •2y-5•2
• 16x8y-10 = 16x8
• y10
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Example – Power of Quotient
2
5s
r
25
2
s
r 10
2
s
r 102sr
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Properties of Exponentsa&b are real numbers, m&n are integers
• Power of Quotient: • b≠0 m
mm
b
a
b
a
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Properties of Exponentsa&b are real numbers, m&n are integers
• Product Property: am * an=am+n
• Quotient of Powers: am = am-n; a≠0 an
Power of a Power Property: (am)n=amn
• Power of a Product Property: (ab)m=ambm
• Negative Exponent Property: a-m= ; a≠0
• Zero Exponent Property: a0=1; a≠0• Power of Quotient: b≠0
m
mm
b
a
b
a
ma
1
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Multiplying and Dividing Monomials• Monomial – an expression that is either
a numeral, a variable or a product of numerals and variables with whole number exponents.
• Constant – Monomial that is a numeral. Example - 2
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Journal Entry:Describe the rules for the follwoing
Power of a Power Property:
• Power of a Product Property:
• Power of Quotient:
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Multiplying Monomials
• (-2x4y2) (-3xy2z3) =
• (-2)(-3)(x4x )(y2y2 ) z3
• 6x5y4 z3
• (-2x3y4) 2 (-3xy2)
• (-2 ) 2 x3∙2y4∙2 ) (-3xy2)
• (4)(-3)(x6x) (y8 y2 )
• -12x7y10
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Scientific Notation
• A number is expressed in scientific notation when it is written as the product of a factor and a power of 10. The factor must be greater than or equal to 1 and less then 10
• a x 10ⁿ, where 1 ≤ a < 10
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Scientific Notation
• 131,400,000,000=
1.314 x 1011
Move the decimal behind the 1st number
How many places did you have to move the decimal?
Put that number here!
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Write using scientific notation
• 12,300=
• 1.23 x 104
• Write using standard notation
• 1.76 x 103
• 1,760
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Example – Scientific Notation
• 131,400,000,000 =• 5,284,000
1.314 x 1011 =
5.284 x 106
61110*284.5
314.1 900,2410*249. 5
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Example – Scientific Notation
• (5.2 x 109)(3.0 x 10-3 )=
• (5.2 x 3.0) (109 x 10-3 )=
• 15.6 x 106
• 1.56 x 107
• 2.45 x 10-3 =
• 0.00245
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Properties of Exponentsa&b are real numbers, m&n are integers
• Product Property: am * an=am+n
• Quotient of Powers: am = am-n; a≠0 an
Power of a Power Property: (am)n=amn
• Power of a Product Property: (ab)m=ambm
• Negative Exponent Property: a-m= ; a≠0
• Zero Exponent Property: a0=1; a≠0• Power of Quotient: b≠0
m
mm
b
a
b
a
ma
1