hw chapter 8 exponents - algebra1kraus / home page€¦ · · 2018-04-064 5 3 r s t r s t 67 5 48...

Simplify each of the following:

1 2 7( )( )x x x 2

2 3 66 ( )( )a a a

3 4(6 )(2 )x x 4

4 2(3 )( 2 )cd c

Simplify each of the following assuming

that no denominator is equal to zero.

Leave NO negative exponents.

5 5

3

x

x 6

7

6

9

3

r

r

7 6

6

3

y

y 8

7 4

5 9

x y

x y


9 3

2x 10 4( 3x)

11 2( 6p) 12

323pq

Simplify each expression.

13 2 7

5

6 4

3

x x

x

14 3

4 23x y

15 2

5 4x

16

23

4

2x

3x




17 3 2 2

4 5 3

r s t

r s t

18 6 7

5

48

6

a y

ab

19 3 2

4 5

7

21

w u

w u

20 11 7

5 9

8

2

a b

a b

21 3 28

32

x y

xy

HW Chapter 8 Exponents

22 The length of a rectangle is 23x y units.

The width of the rectangle is 3 24x y units.

What is the area of the rectangle?

23 Given the following dimensions of a

rectangle, find the area.

4 3x y

43xy

24 The area of a rectangle is 5 412x y units.

If the length is 2 34x y units, find the

width of the rectangle.

25 The length of a side of a square is

32a b units. Find the area of the square.


26 2 2 3( 3k m )( 2k m) 27

2 4( 5a b)(3a )

28 4 31( 15ax )( ax )

3 29

2 3 2(cd )(c d )

30 Simplify the following:

4 92 2


31 2(5t) 32 3

2 25x y

33 5

gh 34 2

3cd

35 Write the equation that represents the

following graph.

36 What do we call the graph in #35?

37 Determine if the following is correct.

If not, explain why and rework it

correctly.

3 5( 12 )( 12 )

15(-12)

38 Explain the steps that should be used

to simplify the following expression

and simplify it.

2

2 32a b

39 Simplify:

3

25x

40 Simplify:

2 2(2a b)( 4ab )

41 Which expression is equivalent

to 6

11 ?

A 2 3

11 11

B 4

211

C 1 6

11 11

D 2 4

11 11

42 Evelyn is going to buy a new computer

for $1100, including tax. She will pay

for the computer by making monthly

payments of $60. If Evelyn has made

p payments, which equation best

describes b, the remaining balance?

A 60 1100 b p

B 1100 60 b p

C 1100 60 b p

D 60 1100 b p

43 The area of a parallelogram is 6 635p q

square units. If the base of the

parallelogram measures 25pq units,

what is the height of the parallelogram?

( 0p and 0q )

44 Which expression is equivalent to

3 5

5 2

15

3

x y

x y?

F 3

2

5y

x

G 5x

y

H 2

3

5

3

y

x

J 3

2

5y

x

45 If 3y x ,what is equivalent to 12x ?

A 36y

B 15y

C 9y

D 4y

Simplify each expression:

46 4 3

4

w u

w u

47 10 5

11 5

2

10

a b

a b

48 8

2 7

24

8

kd

k d

49 12 8

14 6

48

16

r s

r s

50 What is the simplified form of 2 7

3 2 2

e f g

e f g?

F 5ef g H 5 9 3e f g

G 5f

eg J

9

5 3

f

e g

51 Explain the steps that should be used

to simplify the following expression.

3 5

6

8 2

4

x x

x

Determine if the following are correct.

If not, rework it correctly.

52 2 3 2214x

7x y y

5 24x y

53

231

cd4

2 51

8c d

54 The area of a rectangle is 11 530m n

square units. If the length of the

rectangle is 4 26m n units, how many

units wide is the rectangle? ( 0m and

0n )

A 7 35m n units

B 7 924m n units

C 15 736m n units

D 15 7180m n units

Find the missing exponent for the

following.

55 9 ? 12b b b

56 2 ? 95 5 25a a a

57 4

? 202 16c c

58 ?

4 3 113 5 45d d d

59 ?

3 24e e

60 Which equation best describes the

relationship between the corresponding

values of x and y shown in the table?

F 10y x

G 2 6y x

H 3 6y x

J 2 8y x

61 The side length of a square is 3 44x yz

units. What is the area of the square?

62 Which expression describes the area in

square units of a rectangle that has a

width of 3 24x y and a length of 2 33x y ?

F 6 612x y

G 5 512x y

H 6 67x y

J 5 57x y

x y

2 12

0 6

1 3

4 6

63 What is an equation for the line passing

through the point T and having a slope of

2 ?

A 2 2y x T

B 2y x

C 2 2y x

D 2y x




64 4 9

5 8

9

15

x y

x y 65 3 7x x

66 2 43 5x x 67 2

47 2x

68 Which of the following expression is

equivalent to 312

4

x y

xy?

A 28x

B 23x

C 23x y

D 33x y

69 What is the simplified form of

3

9

3d

?

F 3

9

27d

G 3243d

H 3

1

243d

J 33d

70 Simplify the following: 3

24 5x

71 The area of a triangle is 3 510x y square

units, and the base of the triangle is

35xy units long. What is the triangle’s

height?

F 2 22x y units

G 4 825x y units

H 2 24x y units

J 4 84x y units

Find the missing exponent for the

following:

72 5 ? 11x x x

73 ?

2 83 81x x

74 ? 8 146 7 42x x x

75 ?

3 4 192 6 192x x x

76 What is the volume of a cube with an

edge length of 22

5x units?

A 68 cubic units

125x

B 44 cubic units

25x

C 62 cubic units

5x

D 424 cubic units

25x

77 Which expression describes the area in

square units of a rectangle that has a

width of 34x y and a length

of 2 36x y ?

F 5 410x y

G 6 324x y

H 6 310x y

J 5 424x y

Simplify each expression:

78 0

2

16

4

=

79 4 7

6

4 5

10

x x

x =

80

02 2

2 3

12

2

d ef

de f

=

81 4 63 3 =

82

32 41

3x y

=

83 2 6

1

8x y =

84 Which expression simplifies to 42x ?

A 42x

B

4

32

2x

C 4

1

2x

D 4

8

4x

85 Solve the inequality and graph.

5 10 15 45x x

86 Use the function to find the next 5

terms.

10

.03

NEXT NOW

NOW

87 Write an equation for the table first

using NEXT/NOW notation and then

as an exponential function.

x -1 0 1 2

y 50 10 2 0.4




x -1 0 1 2

y 25 125 625 3125


terms.

1

3

9

NEXT NOW

NOW

Simplify the expressions

90 2 6t t

91 2(5 )xy

92 2

6p

93

4

2

s

t

94 3

5 25r r

95

2

0 6 38y x y

96 Write an equation for the list of

values using NEXT/NOW notation

and then use it to find the 8th term.

36 12 4 1.3

97 Solve the system

9 4 26

18 7 22

x y

x y

Identify each function as linear,

exponential growth, or exponential decay

98 1

43

xy 99 1

23

y x

100 .5xy 101 1

43

x

y

102 2 3y x 103 6y x

104 100(.47)xy 105 .47(100)xy

106 The Greens bought a condominium for

$83,000. Assuming that its value will

appreciate 6% per year, how much will

the condo be worth in five years when

they are ready to move again?

For each of the following identify the

growth factor and the growth rate.

107 3(1.68)xy

108 1

32

xy

109 (1 )xy a b

110One computer industry expert reported

that there were about 200,000,000

computers worldwide in 2001 and that

the number was increasing at an

annual rate of about 10%. What is the

number of computers that will be in

use in 2009?


terms.

4

.5

NEXT NOW

NOW

112 Ten years ago, Mr. and Mrs. Boyce

bought a house for $96,000. The value

of their house appreciated at a steady

rate of 3%. What is the value of their

house now?

113 Identify the function as growth or

decay and write the equation to

model it.

(0, 2) (1, 5)

Use the equation .6(1.1)xy

114 Does it represent exponential

growth or decay?

115 Find the value when x = -4

116 Find the value when x = 2



model it.



model it.

119 A piece of machinery valued at

$2,500 depreciates at a steady rate

of 10% yearly. The owner plans to

replace the equipment after 15

years. What will the depreciated

value be at this time?

120 Shayna has a total of 50 music CDs in

two categories. The number of her

rock CDs is 8 more than twice the

number of her country CDs. Which

system of equations can be used to

find how many rock CDs, r, and

country CDs, c, Shayna has?

A r = 2c

r − 50 = c

B r − c = 50

c = 2r + 8

C r + c = 50

r = 2c + 8

D r + c = 50

c = 2r − 8



model it.

(0, 1) (1, 6)

(0, 1)

(1, .75)

(0, 4)

(1, 1)




x -1 0 1 2

y 1/8 1/4 1/2 1

Use the equation 2(.75)xy

123 Does it represent exponential

growth or decay?

124 Find the value when x = -4

125 Find the value when x = 2

126 Zeller Industries bought a piece of

weaving equipment for $50,000. It

is expected to depreciate at a steady

rate of 10% per year. What will the

value be after 6 years?

For each of the following identify the

decay factor and the decay rate.

127 3(.68)xy

128 1

.32

xy

129 (1 )xy a b


terms.

4

16

NEXT NOW

NOW

131 Kyle has saved $500 of the money he

earned working at Carousel Music. If

he spends 10% of the money each

week, how much money will he have

left after 6 weeks?

Simplify the expressions

132

3

1

5z

133

2 5

3 7

(6 )x y

x y

134 4

4x

135 2

2 54 3p p

136

22

16

4

xz

z

Compare each of the following with the

graph of the function

1

8

x

y

137

12

8

x

y 138

1

8

x

y

139

1 1

4 8

x

y 140

13

8

x

y

Tell whether the points would lie on

the graph of an exponential growth or

exponential decay. Write a rule for the

function.

141 0,6 and 1,4.8

142 0,8 and 1,4.8

143 0,6 and 1,12.8

144 Write the equation of the line that

passes through the points (-3,6) and

(5,46).

145 In 2003 a family bought a boat for

$4000. The boat depreciates at a

rate of 7% annually. In 2006 a

person offers to buy the boat for

$3000. Should the family sell the

boat?

Compare each of the following with the

graph of the function 3xy

146 4 3xy 147 2.5 3xy

148 1

34

xy 149 3xy

150 If a population triples each year,

what is the growth factor? Growth

rate?

151 There are 25 students in Ms. Leo’s

math class. The ratio of boys to girls is

2:3. Which equation can be used to

determine g, the number of girls in

Ms. Leo’s class?

A 2 g

=5 25

B 3 g

=5 25

C 2 g

=3 25

D 3 25

=5 g

152 Solve the system

5 2 16

3 4 20

x y

x y

REVIEW

1 Simplify: 2 3y y y

2 Simplify:

3 6

5 9

18

3

a b

a b

3 Simplify:

6 2

5

12

18

x y

x y

4 Simplify: 0

3

14

5

5 Simplify: 8 2 35 3a b a b

6 The area of a rectangle is 3 942x y units

and the width of the rectangle is 2 67x y

units. Write an expression that

describes the length of the rectangle?

7 Simplify: 5

ab

8 Simplify: 3

2 512 s t

9 Simplify:

04

5

13

18

r

r

10 Simplify:

3 4

6 2 5

5

35

a b c

a b c

11 Find the missing exponent for the

following.

A 3 ? 3 13p p p p

B 3 ? 2 84 3 5 60x x x x

C ?

3 96 216x k

D ?

2 112 9 288g g g

12 Simplify: 2 4 3221

3x y x y

13 Simplify:

3

2

8

4h

14 Simplify: 3 2

4 5

2 3

18

a b b

a b

15 Find the area of a square if the length

of a side measures 2 38g h units.

16 Simplify: 3

3 4 2 25a b c ab c

17 A race car driver bought a car for

$85,000. The car will depreciate at a

steady rate of 11% yearly. The owner

plans to drive the car for 5 years.

What will the depreciated value be at

this time? (round to the nearest dollar)


terms.

.4

25

NEXT NOW

NOW




x -1 0 1 2

y 18 9 4.5 2.25



model it.

(0, 6)

(1, 2)

21 Use the equation 16(.25)xy

Does it represent exponential

growth or decay?

Find the value when x = 4

Find the value when x = -2

22 Identify the growth factor and the

growth rate.

A 3(1.68)xy B 1

32

xy

23 Eight years ago, Dan & Suzanne

bought land to build a house on near

Possum Kingdom for $230,000. The

value of their land appreciated at a

steady rate of 3%. What is the value

of their land today? (round to the nearest dollar)

24 Compare each of the following with

the graph of the function 2xy

A 1

24

xy B 2.5 2xy

C 4 2xy D 2xy

hw chapter 8 exponents - algebra1kraus / home page€¦ · · 2018-04-064 5 3 r s t r s t 67 5 48...

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