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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0011 0010 1010 1101 0001 0100 1011

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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0011 0010 1010 1101 0001 0100 1011

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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0011 0010 1010 1101 0001 0100 1011

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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0011 0010 1010 1101 0001 0100 1011

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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0011 0010 1010 1101 0001 0100 1011

Question #11

• Simplify the expression:

a. -3a5 b. -16a5

c. -3a8 d. -16a8

24a10

8a2

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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