A.9 Properties of Exponents 2010
September 20, 2010
A.9 Properties of Exponents
Objective:
Use properties of exponents to simplify algebraic expressions. Jan 17­11:15 AM
1
A.9 Properties of Exponents 2010
September 20, 2010
Warm­up
Fill in the table with fractional answers.
2x
10x
5x
22 = 52 =
102 =
21 =
51 =
101 =
20 =
50 =
100 =
2­1 =
5­1 =
10­1 =
2­2 =
5­2 =
10­2 =
Jan 17­11:20 AM
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A.9 Properties of Exponents 2010
September 20, 2010
From your warm­up, you should have discovered the following two properties:
For every nonzero number a, a0 = 1
For every nonzero number a and integer n,
a­n = 1n
a
Jan 17­11:20 AM
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A.9 Properties of Exponents 2010
September 20, 2010
Simplify the following:
1. 4­3 = 2. (­4)­3 = 3. 70 = 4. 7­1 = Jan 17­11:20 AM
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A.9 Properties of Exponents 2010
September 20, 2010
GENERAL RULE m
n
a a = a
m + n
Multiplication with Powers
TRY SOME
Jan 17­11:54 AM
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A.9 Properties of Exponents 2010
September 20, 2010
Simplify.
1. (5x5)(3y6)(3x2) = 2. a6b3 a2b­2 =
3. c­2c7 = 4. ­m2 4r3 12r­4 5m =
Jan 17­11:58 AM
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A.9 Properties of Exponents 2010
September 20, 2010
GENERAL RULE n
n
n
(ab) = a b
Product to a Power
TRY SOME
Jan 17­12:26 PM
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A.9 Properties of Exponents 2010
September 20, 2010
Simplify.
1. (­2x­1y2)3 =
2. (­a2b3c)4 =
3. (a­1b2)2(a3b4)­2 = Jan 17­12:31 PM
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A.9 Properties of Exponents 2010
September 20, 2010
Power Raised to a Power
GENERAL RULE
m n
m n
(a ) = a
TRY SOME
Jan 17­12:04 PM
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A.9 Properties of Exponents 2010
September 20, 2010
Simplify these!
1. (2z3)4 = 2. (d3)5(d3)0 =
3. (x3)­1(x2)5 =
4. (q10)10 =
5. (3b­2)2(a2b4)3 = Jan 17­12:06 PM
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A.9 Properties of Exponents 2010
September 20, 2010
Division with Powers
GENERAL RULE
m
a
m­n
n = a
a
TRY SOME
Jan 17­12:49 PM
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A.9 Properties of Exponents 2010
September 20, 2010
Try these!
1. a14 =
a6
2.
c­1d3
=
c5d­4
3.
x2y­1z4
=
xy4z­3
4.
m­1n2
=
m3n
Jan 17­12:50 PM
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A.9 Properties of Exponents 2010
September 20, 2010
Quotient to a Power
GENERAL RULE
a n an
= n
b
b
TRY SOME
Jan 17­12:52 PM
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A.9 Properties of Exponents 2010
September 20, 2010
Try some more!
2
1. 3
x2
2.
x
y2
3
3. a
b
­n
=
=
=
Jan 17­12:53 PM
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A.9 Properties of Exponents 2010
September 20, 2010
Make sure you have written down all the properties of exponents.
Jan 17­10:49 AM
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A.9 Properties of Exponents 2010
September 20, 2010
HOMEWORK:
Properties of Exponents Worksheet
Jan 17­12:58 PM
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