AA Section 7-2/7-3
Post on 22-Apr-2015
771 Views
Preview:
DESCRIPTION
Transcript
Section 7-2 (and 7-3)Properties of Powers (and Negative Integer Exponents)
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?
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)
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
Example 1
32i34
Example 1
32i34
= (3i3)(3i3i3i3)
Example 1
32i34
= (3i3)(3i3i3i3) = 36
Example 1
32i34
= (3i3)(3i3i3i3) = 36
32i34
Example 1
32i34
= (3i3)(3i3i3i3) = 36
32i34
= 32+4
Example 1
32i34
= (3i3)(3i3i3i3) = 36
32i34
= 32+4 = 36
Product of Powers Postulate
bmibn = bm+n
Example 2
(32 )4
Example 2
(32 )4 = (32 )(32 )(32 )(32 )
Example 2
(32 )4 = (32 )(32 )(32 )(32 ) = 38
Example 2
(32 )4 = (32 )(32 )(32 )(32 ) = 38
(32 )4
Example 2
(32 )4 = (32 )(32 )(32 )(32 ) = 38
(32 )4 = 32i4
Example 2
(32 )4 = (32 )(32 )(32 )(32 ) = 38
(32 )4 = 32i4
= 38
Power of a Power Postulate
(bm )n = bmn
Example 3
(x2 y )3
Example 3
(x2 y )3 = (x2 y )(x2 y )(x2 y )
Example 3
(x2 y )3 = (x2 y )(x2 y )(x2 y ) = x6 y3
Example 3
(x2 y )3 = (x2 y )(x2 y )(x2 y ) = x6 y3
(x2 y )3
Example 3
(x2 y )3 = (x2 y )(x2 y )(x2 y ) = x6 y3
(x2 y )3 = (x2 )3 y3
Example 3
(x2 y )3 = (x2 y )(x2 y )(x2 y ) = x6 y3
(x2 y )3 = (x2 )3 y3
= x6 y3
Power of a Product Postulate
(ab)m = ambm
Example 4
(3x2 y3 )4
Example 4
(3x2 y3 )4 = 34(x2 )4 (y3 )4
Example 4
(3x2 y3 )4 = 34(x2 )4 (y3 )4 = 81x8 y12
Example 5
1011
108
Example 5
1011
108 =
(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)
Example 5
1011
108 =
(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)
Example 5
1011
108 =
(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)(10)
= 103
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
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
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
Quotient of Powers Postulate
bm
bn= bm−n
Example 6
x
y
⎛
⎝⎜⎞
⎠⎟
6
Example 6
x
y
⎛
⎝⎜⎞
⎠⎟
6
=
x
y
⎛
⎝⎜⎞
⎠⎟x
y
⎛
⎝⎜⎞
⎠⎟x
y
⎛
⎝⎜⎞
⎠⎟x
y
⎛
⎝⎜⎞
⎠⎟x
y
⎛
⎝⎜⎞
⎠⎟x
y
⎛
⎝⎜⎞
⎠⎟
Example 6
x
y
⎛
⎝⎜⎞
⎠⎟
6
=
x
y
⎛
⎝⎜⎞
⎠⎟x
y
⎛
⎝⎜⎞
⎠⎟x
y
⎛
⎝⎜⎞
⎠⎟x
y
⎛
⎝⎜⎞
⎠⎟x
y
⎛
⎝⎜⎞
⎠⎟x
y
⎛
⎝⎜⎞
⎠⎟ =
x6
y6
Power of a Quotient Postulate
a
b
⎛
⎝⎜⎞
⎠⎟
m
=am
bm
Example 7
x3
x3
Example 7
x3
x3 = x3−3
Example 7
x3
x3 = x3−3 = x0
Example 7
x3
x3 = x3−3 = x0
x3
x3
Example 7
x3
x3 = x3−3 = x0
x3
x3 = 1
Example 7
x3
x3 = x3−3 = x0
x3
x3 = 1
x0 = 1
Zero Exponent Theorem
b0 = 1, b ≠ 0
7-3: Negative Integer Exponents
Example 1
x7
x10
Example 1
x7
x10 = x7−10
Example 1
x7
x10 = x7−10 = x−3
Example 1
x7
x10 = x7−10 = x−3
x7
x10
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 )
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 )
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
Negative Exponent Theorem
b−n =
1
bn
Example 2
(5b)3 (4b)−5
Example 2
(5b)3 (4b)−5
=
(5b)3
(4b)5
Example 2
(5b)3 (4b)−5
=
(5b)3
(4b)5 =
125b3
1024b5
Example 2
(5b)3 (4b)−5
=
(5b)3
(4b)5 =
125b3
1024b5
=
125
1024b2
Homework
Homework
p. 430 #14-30p. 435 #9-21, 25
top related