WARM UP

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WARM UP

• Evaluate when x 4

1. x x x
64
2. (14 x )2
100
3. x x x2
256
4. (-x) (-x)
16
5. -x2
-16
6. (-x)2
16
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Section 8.1Multiplication Propertiesof
Exponents
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Multiplication Properties of Exponents
Product of Powers Property To multiply powers
having the same base, add the exponents.
am an amn
x2 x6 x26 x8
22 23 223 25 32
22 23 4 8 32
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Multiplication Properties of Exponents
Power of a Power Property To find the power of
a power, multiply the exponents.
(am)n a m n
(x2)6 x2 6 x12
(22)3 22 3 26 64
(22)3 43 64
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Multiplication Properties of Exponents
Note When you use the Power of a Power
Property, it is the quantity within parenthesis
that is raised to the power, not the individual
terms.
(x 2)3 (x 2) (x 2) (x 2)
(x 2)3 does not equal x3 23
(3 2)3 (3 2) (3 2) (3 2) 125
(3 2)3 does not equal 33 23 or 35.
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Multiplication Properties of Exponents
Power of a Product Property To find the power
of a product, find the power of each factor and
multiply.
(a b)n an bn
(a b)3 a3 b3
(2 3)3 23 33 8 27 216
(2 3)3 63 216
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Examples
53 56
59
3 35
36
x2 x3 x4
x9
(-2) (-2)4
(-2)5
(52)3
56
(x3)4
x12
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Examples(continued)
((-2)3)5
(-2)15
x x x
x3
(3 4)2
32 42
(3xy)4
34 x4 y4
(-3y)2
(-3)2 y2 9y2
-(3y)2
- (3)2 y2 -9y2
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Examples(continued)
(3x4y)2 y5
32x8y2y5 9x8y7
(2x2y)5 x6
25x10y5x6 32x16y5
2x4 (3x)2
2x4 32x2 2 9x6 18x6
(a7b2) (a4b9)3
a7 b2 a12 b27 a19 b29
(-2x4)3 (-x8)2
(-2)3x12 (-1)2x16 -8x28
(3x3)4 (x3)2
34x12 x6 81x18
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Examples(continued)
(-3xy)4 (-x3)
(-3)4x4y4(-1)x3 -81x7y4
(-xy2) (x2y)3
(-1)xy2x6y3 -x7y5