aa section 7-2/7-3
DESCRIPTION
Properties of PowersTRANSCRIPT
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Section 7-2 (and 7-3)Properties of Powers (and Negative Integer Exponents)
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Warm-upA multiple choice quiz has two questions. For each
question, there are three choices: A, B, and C. List all possible ways for a student to complete the quiz.
Is the possible number of ways 23 or 32?
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Warm-upA multiple choice quiz has two questions. For each
question, there are three choices: A, B, and C. List all possible ways for a student to complete the quiz.
Is the possible number of ways 23 or 32?
(1A, 2A), (1A, 2B), (1A, 2C), (1B, 2A), (1B, 2B), (1B, 2C), (1C, 2A), (1C, 2B), (1C, 2C)
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Warm-upA multiple choice quiz has two questions. For each
question, there are three choices: A, B, and C. List all possible ways for a student to complete the quiz.
Is the possible number of ways 23 or 32?
(1A, 2A), (1A, 2B), (1A, 2C), (1B, 2A), (1B, 2B), (1B, 2C), (1C, 2A), (1C, 2B), (1C, 2C)
32
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Example 1
32i34
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Example 1
32i34
= (3i3)(3i3i3i3)
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Example 1
32i34
= (3i3)(3i3i3i3) = 36
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Example 1
32i34
= (3i3)(3i3i3i3) = 36
32i34
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Example 1
32i34
= (3i3)(3i3i3i3) = 36
32i34
= 32+4
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Example 1
32i34
= (3i3)(3i3i3i3) = 36
32i34
= 32+4 = 36
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Product of Powers Postulate
bmibn = bm+n
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Example 2
(32 )4
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Example 2
(32 )4 = (32 )(32 )(32 )(32 )
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Example 2
(32 )4 = (32 )(32 )(32 )(32 ) = 38
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Example 2
(32 )4 = (32 )(32 )(32 )(32 ) = 38
(32 )4
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Example 2
(32 )4 = (32 )(32 )(32 )(32 ) = 38
(32 )4 = 32i4
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Example 2
(32 )4 = (32 )(32 )(32 )(32 ) = 38
(32 )4 = 32i4
= 38
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Power of a Power Postulate
(bm )n = bmn
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Example 3
(x2 y )3
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Example 3
(x2 y )3 = (x2 y )(x2 y )(x2 y )
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Example 3
(x2 y )3 = (x2 y )(x2 y )(x2 y ) = x6 y3
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Example 3
(x2 y )3 = (x2 y )(x2 y )(x2 y ) = x6 y3
(x2 y )3
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Example 3
(x2 y )3 = (x2 y )(x2 y )(x2 y ) = x6 y3
(x2 y )3 = (x2 )3 y3
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Example 3
(x2 y )3 = (x2 y )(x2 y )(x2 y ) = x6 y3
(x2 y )3 = (x2 )3 y3
= x6 y3
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Power of a Product Postulate
(ab)m = ambm
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Example 4
(3x2 y3 )4
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Example 4
(3x2 y3 )4 = 34(x2 )4 (y3 )4
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Example 4
(3x2 y3 )4 = 34(x2 )4 (y3 )4 = 81x8 y12
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Example 5
1011
108
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Example 5
1011
108 =
(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)
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Example 5
1011
108 =
(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)
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Example 5
1011
108 =
(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)
= 103
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Example 5
1011
108 =
(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)
= 103
1011
108
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Example 5
1011
108 =
(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)
= 103
1011
108 = 1011−8
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Example 5
1011
108 =
(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)
= 103
1011
108 = 1011−8 = 103
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Quotient of Powers Postulate
bm
bn= bm−n
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Example 6
x
y
⎛
⎝⎜⎞
⎠⎟
6
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Example 6
x
y
⎛
⎝⎜⎞
⎠⎟
6
=
x
y
⎛
⎝⎜⎞
⎠⎟x
y
⎛
⎝⎜⎞
⎠⎟x
y
⎛
⎝⎜⎞
⎠⎟x
y
⎛
⎝⎜⎞
⎠⎟x
y
⎛
⎝⎜⎞
⎠⎟x
y
⎛
⎝⎜⎞
⎠⎟
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Example 6
x
y
⎛
⎝⎜⎞
⎠⎟
6
=
x
y
⎛
⎝⎜⎞
⎠⎟x
y
⎛
⎝⎜⎞
⎠⎟x
y
⎛
⎝⎜⎞
⎠⎟x
y
⎛
⎝⎜⎞
⎠⎟x
y
⎛
⎝⎜⎞
⎠⎟x
y
⎛
⎝⎜⎞
⎠⎟ =
x6
y6
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Power of a Quotient Postulate
a
b
⎛
⎝⎜⎞
⎠⎟
m
=am
bm
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Example 7
x3
x3
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Example 7
x3
x3 = x3−3
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Example 7
x3
x3 = x3−3 = x0
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Example 7
x3
x3 = x3−3 = x0
x3
x3
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Example 7
x3
x3 = x3−3 = x0
x3
x3 = 1
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Example 7
x3
x3 = x3−3 = x0
x3
x3 = 1
x0 = 1
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Zero Exponent Theorem
b0 = 1, b ≠ 0
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7-3: Negative Integer Exponents
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Example 1
x7
x10
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Example 1
x7
x10 = x7−10
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Example 1
x7
x10 = x7−10 = x−3
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Example 1
x7
x10 = x7−10 = x−3
x7
x10
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Example 1
x7
x10 = x7−10 = x−3
x7
x10 =
(x )(x )(x )(x )(x )(x )(x )(x )(x )(x )(x )(x )(x )(x )(x )(x )(x )
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Example 1
x7
x10 = x7−10 = x−3
x7
x10 =
(x )(x )(x )(x )(x )(x )(x )(x )(x )(x )(x )(x )(x )(x )(x )(x )(x )
=
1(x )(x )(x )
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Example 1
x7
x10 = x7−10 = x−3
x7
x10 =
(x )(x )(x )(x )(x )(x )(x )(x )(x )(x )(x )(x )(x )(x )(x )(x )(x )
=
1(x )(x )(x )
=1
x3
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Negative Exponent Theorem
b−n =
1
bn
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Example 2
(5b)3 (4b)−5
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Example 2
(5b)3 (4b)−5
=
(5b)3
(4b)5
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Example 2
(5b)3 (4b)−5
=
(5b)3
(4b)5 =
125b3
1024b5
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Example 2
(5b)3 (4b)−5
=
(5b)3
(4b)5 =
125b3
1024b5
=
125
1024b2
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Homework
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Homework
p. 430 #14-30p. 435 #9-21, 25