properties of exponents examples and practice. product of powers property how many factors of x are...
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42510011 0010 1010 1101 0001 0100 1011
Properties of Exponents
Examples and Practice
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Product of Powers Property
• How many factors of x are in the product x3∙x2?
• Write the product as a single power.
• In general:
5 factors: x∙x∙x∙x∙x
x∙x∙x∙x∙x = x5
xm∙xn= xm + n
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0011 0010 1010 1101 0001 0100 1011
Question #1
• Simplify the expression:
a3a5
a. a15 b. a8
c. a2 d. 1/a2
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Question #2
• Simplify the expression:
(3m2)(2m4)
a. 6m8 b. 5m6
c. 5m8 d. 6m6
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0011 0010 1010 1101 0001 0100 1011
Question #3
• Simplify the expression:
(-2xy3)(5x4y2)
a. -10x5y5 b. -10x4y5
c. 3x5y5 d. -10x4y6
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0011 0010 1010 1101 0001 0100 1011
Power of a Power Property
• How many factors of x are in the expression (x3)2?
• Write the product as a single power.
• In general:
6 factors: x∙x∙x∙x∙x∙x
(x∙x∙x)∙(x∙x∙x) = x6
(xm)n= xm∙n
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Question #4
• Simplify the expression:
(42)5
a. 47 b. 1610
c. 410 d. 167
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0011 0010 1010 1101 0001 0100 1011
Question #5
• Simplify the expression:
(x3)4
a. x7 b. 2x7
c. x12 d. 2x12
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0011 0010 1010 1101 0001 0100 1011
Power of a Product Property
• How many factors of x and y are in the expression (xy)2?
• Simplify the expression.
• In general:
2 factors of each: (x∙y)∙(x∙y)
(x∙y)∙(x∙y) = x2y2
(x∙y)m= xmym
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0011 0010 1010 1101 0001 0100 1011
Question #6
• Simplify the expression:
(b3c2)4
a. b7c6 b. b12c8
c. b7c8 d. 2b12c8
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Question #7
• Simplify the expression:
(-3a3b)2
a. 6a5b2 b. 9a5b2
c. -9a6b2 d. 9a6b2
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0011 0010 1010 1101 0001 0100 1011
Question #8
• Simplify the expression:
(-3a3b)2(2ab)
a. 36a7b3 b. 18a7b3
c. -6a7b3 d. -18a7b3
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0011 0010 1010 1101 0001 0100 1011
Quotient of Powers Property
• Simplify the expression.
• In general:
5
3
x
x
52
3
x x x x x xx
x x x x
mm n
n
xx
x
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Question #9
• Simplify the expression:
a. a5 b. a9
c. 1/a5 d. 1/a9
a7
a2
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0011 0010 1010 1101 0001 0100 1011
Question #10
• Simplify the expression:
a. a5 b. 6
c. 1/a5 d. 1/6
a
a6
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Question #11
• Simplify the expression:
a. -3a5 b. -16a5
c. -3a8 d. -16a8
24a10
8a2
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0011 0010 1010 1101 0001 0100 1011
Question #12
• Simplify the expression:
a. b.
c. d. 0.75a4b3
6a4b7c 2
8a8b4c 2
6b3
8a2
3b3
4a4
3b3c
4a4
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0011 0010 1010 1101 0001 0100 1011
Power of a Quotient Property
• Simplify the expression.
• In general:
2x
y
2 2
2
x x x x
y y y y
m m
m
x x
y y
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0011 0010 1010 1101 0001 0100 1011
Question #13
• Simplify the expression:
a. b.
c. d. 0.2
42
3
8
12
16
81
2
3
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0011 0010 1010 1101 0001 0100 1011
Question #14
• Simplify the expression:
a. b.
c. d.
22 5
32
x y z
x
4 10
62
x y z
x
4 7 3
54
x y z
x
4 10 2
64
x y z
x
4 10
64
x y z
x
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0011 0010 1010 1101 0001 0100 1011
Zero Exponent Property
• In general:
0 1a
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Question #15
• Simplify the expression: x0y2
a. b. xy2
c. y2 d.
2
1
y
2
x
y