8.2 P.O.D. Simplify the following expressions.

1. 2(y2)5

2. 3x3 + 2x3

3. (2x)(4x2)(-10x3)

4. 3(x3)5

5. -3x2 + x4

Quotients of Powers

Section 8.3

Big Idea

• Because of the relationship between multiplication and division, quotients of powers can be themselves written as powers

Goal• Develop and apply the Quotient of Powers

Property

HW Answers 8.2

Quotient of Powers

• By expanding the exponent and cross cancelling you can simplify division of powers.

• EX:

• Can you think of a short cut to get the same result?

53

2

x x x x x xx x x x

x x x

Quotient of Powers Rule: for all non zero b, if you divide two powers with the same bases, you can subtract the exponents.

mm n

n

bb

b

REMEMBER – Coefficients still need to be divided not SUBTRACTED

125 5

7

2015 4

5

xx x

x

1) Change the following to a simplified power:

a. b.

c.

12

3

4

43

12 9

4 1

4 4

13

13

5

5

412-3 = 49 43-12 = 4-9

513-13 = 50 = 1

8.3

2) In March, 1992, there was a total of 283.9 billion dollars in U.S. currency in circulation. The U.S. population was about 252.7 million. how much currency per person was in circulation?

11 11

8 8

283,900,000,000 2.839 10 2.839 10

252,700,000 2.527 10 2.527 10

≈ 1.12347 x 103 ≈ $1,123.47 per person

8.3

3) Simplify

a) b)

c) d)

2 10

15

30

25

x y

xy

7

2

12

3

x

x

14

17

28x10

7x10

5

8

a

a

5

6

5

x

y = 4x5

4·10-3=

1 441000 1000

.004

3

1

a

8.3

Quiz Review: 8-1 through 8-3

1) Fill in the blank with properties of exponents(includes the Quotient of a powers property)

a) bm ∙ bn = b) (bm)n = c) = bm-n d) 49500000 = scientific notation

e) 4.394 x 10-6 =

bm+n bm·n

bm/bn 4.95 x 107

0.000004394

Rev1

2) Simplify an expression.

4 5 1 3

2 4 2 3

56 4

16 7

x y xz x y z

xy z x z

Simplify coefficients, use properties

= 2x4-3y-7+3z5+4 = 2xy-4z9 =

Cancel coefficients, use properties

7

2x4+1-1y-5-2z1-(-4)

4

7x-1-2y3z1-(-3)=

Rev1

9

4

2xz

y

Simplified expressions have no negative exponents

A lot of examples to try:10

6

8

6

6

10

6

1.

2.

3.

504.5

x

x

x

x

x

x

x

x

14

7

2

6 7

2 5

9

9

145.7

306.

5

47.2

188.6

x

x

x

x

x y

x y

x

x

14

7

2

2

5 9

2 2

9

3

39.19

3010.

5

1611.32

1812.

6

x

y

x

x

x y

x y z

x

y

Practice

10

6

(4 )

(4 )

x

x

4(4 )x

Practice

2 3 4( 9 )( 4 )x y x y

6 436x y

Practice

2 4(2 )( 4 )(4 )x x y y

6 232x y

Practice

12 40 23(2 )( 4 )(4 )x x y

758x

Practice

(3 )x y

3xy

Practice

11

8

x

x

3x

Practice

8

yx

x

8yx

Practice

9

11

a

b

9

11

a

b

Practice

9 13

2 11

x y

x y

7 2x y

Practice

8

7

20

4

y

y

5y

Practice

1022

2

y

y

911y