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8-1B Lesson Master
Questions on SPUR Objectives
See pages 521–523 for objectives.
USES Objective H
1. An art-supply store sells tubes of white paint in 4 sizes and
in 3 different brands. How many different choices of size/brand
are possible?
2. Edward wears jeans, a T-shirt, and a sweatshirt every day to
school. He has 6 pair of jeans, 9 T-shirts, and 4 sweatshirts.
How many different outfits can he wear?
3. Amy, Beth, Carlo, and Dion plan to run for the positions of
president, vice-president, secretary, and treasurer of the
student council. How many ways could the four offices be filled?
4. A combination lock has 50 numbers. The combination consists
of 3 numbers, each of which can repeat. How many different
combinations can be formed?
a. Write your answer in exponential form.
b. Write your answer in base 10.
5. Emma can choose from 50 types of freshwater fish for her new
aquarium. She can also choose from 12 types of artificial plants.
a. If she chooses just one type of plant and one type of fish,
how many different ways can she set up her tank?
b. Write your answer in scientific notation.
6. A math quiz has 8 true-false questions and 17
multiple-choice questions with 4 answer choices.
b. What is the probability of getting all the answers on the quiz
correct by guessing?
Use this information for 7–9. Seven Chicago Bears football fans each
wrote a letter from the phrase “GO BEARS” on their chests to show their
team support. When they arrived at the game they sat next to each
other in random order.
7. How many different forms of the phrase are possible?
8. Write your answer in scientific notation.
9. What is the probability that the fans spelled the phrase
correctly when they first sat down at the game?
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a. How many different answer sheets are possible?
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8-1B
page 2
A bakery offers the following breakfast options.
Doughnuts
Bagels
Muffins
Beverages
Plain
Cinnamon/raisin
Blueberry
Orange juice
Chocolate
Blueberry
Apple
Coffee
Pumpkin
Oatmeal
Chocolate
Tea
Cinnamon
Apple juice
Buttermilk
Banana/nut
10. Gilbert always orders a bagel and a drink. How many different
choices are available?
11. Before Anna gets to school she orders one item to eat and one
item to drink. How many different choices can she make?
Your aunt orders 1 doughnut, 2 bagels, 2 muffins, and 5 drinks for her
and some co-workers.
12. Write the number of ways she can order
a. in exponential form.
b. in base 10.
c. in scientific notation.
Avery and his friends attend the Fall Frolic every year. There are
15 food booths, 20 game booths, 12 rides, and a haunted house.
13. Avery plans to eat some food and play some games. How
many different choices can he make?
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14. Avery’s friend Melody wants to attend one food booth, one
game booth, one ride and the haunted house. How many
different choices does she have?
15. How does the answer to Question 14 change if Melody
wants to attend 2 food booths, 2 game booths, 2 rides, and
the haunted house? She can attend the same booth or ride
more than once.
16. Avery’s parents also attend the festival and intend to eat at
a food booth. What is the probability that they will eat at the
same food booth as Avery?
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8-2B Lesson Master
Questions on SPUR Objectives
See pages 521–523 for objectives.
SKILLS Objective A
In 1–4, an expression is given.
a. Write the expression in expanded form.
b. Write the expression as a single power.
1. 53 · 5
2. x 3 · x 2
a.
a.
b.
b.
3. (−34)2
4. (x 3)5
a.
a.
b.
b.
In 5–25, simplify.
5. a5 · a
6. b2 · b4
7. c7 · −1c 3
8. 2d · 5d 9
9. e 3f 4 · e 2f
10. jk · 3jk2
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11. −2m2n3 · −4m4n5
12. (6p0)3
13. 2q(q 3)4
14. 5(rs)2
15. 3t 0(t 5)5
16. b20 · b5
17. −u24 · uv 3
18. −10x5 · 0.2x 3
19. wx17 · w17x
20. 7y 6z 3 · 3y 2z 3
21. −12c16d 9 · 0.5c0d 7
22. 0.875ef 0 · −16e 2f
23. (9g 2)(9h3)
24. (10i )2(0.01i 9)
25. 16j 10k6 · (0.5j 5k2)3
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page 2
PROPERTIES Objective G
In 26–33, solve for x and y and name the power property used to find the solution.
26. 25 · 2 x = 215
27. 4x · 4x = 410
28. (63)x = 612
29. (7x)x = 7 9
30. (a3 · a x)2 = a6
31. c 4(c 3)x = c10
x
32. de 2 · 3d ey = 3d 3e5
x
33. ( fg) · f 3g 4 = f 9g 10
35. Write a multiplication problem that uses the Power of a Power Property
to get an answer of m20.
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Algebra
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34. Write a multiplication problem that uses the Product of Powers Property
to get an answer of k17.
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8-3B Lesson Master
Questions on SPUR Objectives
See pages 521–523 for objectives.
SKILLS Objective A
In 1 and 2, a fraction is given.
a. Write the numerator and denominator in expanded form.
b. Simplify the fraction.
10j 5k3
2. _____
2
a5
1. __
a2
12j k
a.
a.
b.
b.
In 3–13, simplify.
−c10
3. ___
c7
3.10 × 108
4. ________
3
3.9 × 106
5. _______
3 × 104
3d 3
6. ___
6d
22e5
7. ____
11e3
16f 6
8. ____6
2 × 10
−4f
10
27g
9. ____
18g 4
−24h11
10. _____
7
(−2)x
11. ____
(−2)y
30m8n4
12. ______
5 2
42m n
4
81p r
13. ______
−36pr 4
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9h
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8-3B
page 2
PROPERTIES Objective G
14. Write an algebraic fraction for which you can use the Quotient
of Powers Property to simplify to 3x 5.
In 15–19, use the Quotient of Powers Property to find the value of x.
x
y
15. __
= y11
y3
513
4
16. ___
5x = 5
18mx
6m4
17. ____3 = ____
7
21m
(−4)7
18. ____
= (−4)5
(−4)x
(2y)
19. ____8 = (2y)12
x
(2y)
9
m
20. Amber tried to simplify ___
, and she got m3. Explain the error she made
m3
in simplifying the fraction.
21. Multiple Choice. Which expression can be simplified to 5m2x?
10mx
A ____
2mx
10m3x
B _____
2mx
10m6x
C _____
3x
10m8x
D _____
4x
2m
2m
5
22. Multiple Choice. Consider the equation __
= 56. Which statement
5n
accurately describes the values of m and n?
m
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A m=n
B m = 4 and n = 2
C m+n=6
D m-n=6
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Back to Lesson 8-4
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8-4B Lesson Master
Questions on SPUR Objectives
See pages 521–523 for objectives.
SKILLS Objectives A and B
In 1 and 2, rewrite without negative exponents.
1. x −3 · y −4
2. 3a2b−5
In 3–8, rewrite: a. without fractions; b. without negative exponents.
32c−4
3. ____
16c2
−d−2e2
4. _____
a.
a.
b.
b.
5.
( __f1 )
−3
4
de
(g )
2
6. ___
−2
a.
a.
b.
b.
70h4j−2k3
7. _______
10h9k
4
−56m−6n−1
8. ________
2 6
8m n
a.
a.
b.
b.
In 9–14, give the answer as a simple fraction.
9. 4−3
11.
( __14 )
10. 9−2
−1
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13. (−2)−4
()
12. __56
−2
3
__
14. (75)5
15. Order the following numbers from least to greatest.
( __34 )−2, __163 , (−3)(−4), ( __23 )−4
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8-4B
page 2
PROPERTIES Objective G
In 16–24, use the properties of negative exponents to find the value of x.
p
1
__
16. ___
px = 7
3 x
16
17. __4 = __
9
r −2sx
1
18. ____
= ___
3
2 6
t5
11
19. __
tx = t
−3
()
p
s
rs
wx
8
21. ____
= __
5
2−3w 4
1
20. 2−3 · w x = ___
3
w
8w
( )
2h−9
22. ____
3hx
24.
( __21 )
-1
−3x
16
3h
= ____
2
−14
23. −14j−4k2x = ____
4 10
jk
=2
−2
x
?
26. Multiple Choice. Which expression can be simplified to __
81
4
x −4
A __3 )
(
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Algebra
( )
x3
B __
3
−1
( )−4
3
C __x
( )
3
D __
x3
−1
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4
25. Justin simplified ( _25 ) , and he got __
. Explain the error he made in
25
simplifying the fraction.
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8-5B Lesson Master
Questions on SPUR Objectives
See pages 521–523 for objectives.
SKILLS Objectives A, B and C
In 1–3, simplify and give the answer as a simple fraction.
()
1. 4 __21
4
( 1 )4
2. 96 __4
In 3 and 4, an expression is given.
a. Write the expression in expanded form.
b. Simplify the expression.
3. (−7x)2
2a 3
4. __
5b
a.
a.
b.
b.
( )
In 5–11, simplify and give the answer as a simple fraction.
5. (3y2)3
6. −(2m2)4
7. (−4n5)3
8. −(6pr2)2
9.
11.
2
( ) · ( __43 )5
9
10. __4
( __4c )2
49
3e
___
( __
e )·( 7 )
2
3
In 12–16, rewrite without parentheses and simplify.
( )
−3e5f 7
14. _____
3 9
13. 4(−3c3d4)2
3
( 2h )
−4 ___
h5
15. __
2
7 ·
5e f
( )
k
16. (6j 5k)2 · ___
6
2j
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4
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12. (2a2b)5
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8-5B
page 2
In 17–19, find the area of the figure.
17.
18.
17x2
cm
30
4x2y 3 ft
40 cm
19.
17x in.
x3 in.
25x in.
Area of a trapezoid is found by
1
__
2 · height · (base 1 + base 2).
PROPERTIES Objective G
In 20–22,
a. Tell what value of x will make the statement true for all values of the
variables.
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b. Identify the property that justifies the first step in simplifying the
statement.
15
−32m
20. (−2m3n−1)x = ______
5
n
6m x
72m2
21. 10 · ___3 = ____
6
( 5n )
a.
a.
b.
b.
5n
22. x3 = −27m18n12
a.
b.
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8-6B Lesson Master
Questions on SPUR Objectives
See pages 521–523 for objectives.
SKILLS Objectives D and E
1. The area of a square is 64 square units. What is the length of a side?
In 2–10, write the exact value or approximate the number to the nearest
hundredth.
2. √##
169
3. − √##
441
225
4. √##
5. √#
85
110
6. − √##
7. 81 2
1
__
1
__
1
__
8. 34 2
9. −(196) 2
1
__
10. −(13) 2
In 11–18, evaluate the expression. Write the exact value or
approximate to the nearest hundredth.
1,048 - 24
11. √#####
1
__
12. √###
9 + 64
1
__
13. (16 + 81) 2
14. (25 + 144) 2
15. 3 √#
13 · √#
13
16. −2 √#
6 · √#
6
1
__
2
( ) · ( __107 )
7
17. 4 __
10
1
__
2
19. Find the length of the missing
side of the right triangle.
2
15
18. __3 · __
8
1
__
2
( ) · ( __158 )
1
__
2
20. Veronica needs a new pole for her kite.
What is the height, h, of the kite? Round
to the nearest whole number.
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25 cm
15
x
15 cm
9
h
42.7 cm
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21. If f (y) = 3 √#y √#y , what is f (8)?
22. Which of the expressions below are equal to (48)1/2?
A 4 √#
3
B 2 √#
24
C 2 √#
12
D √#
6 · √#
8
In 23–32, write the exact value or approximate the number to the
nearest hundredth.
3
9.261
23. √###
3
24. √##
125
3
25. √##
−27
26. − √##
343
3
27. √##
512
28.
3
3
3
29. √##
1.2 · √##
1.2 · √##
1.2
3
3
3
30. √#
5 · √#
5 · √#
5
3
3
31. √#
64 · √#
−8
3
3
3
32. √#
27 · √##
−216 · √#
−1
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√#__14 · √#__41 · √#__41
3
3
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8-7B Lesson Master
Questions on SPUR Objectives
See pages 521–523 for objectives.
SKILLS Objective D
In 1–4, evaluate the expression.
1. √#
18 · √#
2
2. √#####
16 · 25 · 225
√#
99
3. ____
√#
73
4. ____
√#
11
√#
7
In 5–7, simplify. Give the exact value. Assume all variables
are positive.
72
5. √#
6. 3 √##
160
7.
12
#
√__
9
In 8 and 9, write the exact value of the unknown in simplified form.
8.
9.
6
3
10
x
y
10. A bowling ball manufacturer created a clear resin ball that can
contain any colored figure. The maximum length of the figure can
s
__
where s represents the surface
be found by the expression 2 √##
4π
area of the ball. What is the length of the figure that can be placed
in a ball with a surface area of 72.25π square inches?
11. Find the exact value of the area of a triangle with a base of
3 inches and a height of √#
6 inches.
4√#
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In 12–23, simplify. Give the exact value. Assume all variables are positive.
12. √###
48a2b2
13. √###
56c2d5
250e 3f 6
14. − √###
15. −2√##
40 x
32y7
16. 5 √##
17. 3 √####
112m4n8p5
##
216h5
_____
24h7
18.
√
20.
###
128s t
√______
50t
4 3
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12n · √##
12n
22. 4 √##
√###
147j 9k2
√###
12j 5k2
19. − _______
10
###
√85xy
21. _______
5 −2
5x y
√###
23. √###
20d4e3 · √##
5d 2e
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8-8B Lesson Master
Questions on SPUR Objectives
See pages 521–523 for objectives.
REPRESENTATIONS Objectives I and J
1. A square has a diagonal with a length of 12 centimeters.
a. Find the length of a side of the square.
b. Find the area of the square.
2. The screen of a projection TV is 41.5 inches long and
28 inches tall. The length of the diagonal of the screen
represents the size of the television. What is the size of
the television?
In 3 and 4, find the area of the figure.
3.
4.
24
25
20
12
In 5 and 6, find the exact length of a side of the cube.
5. A cube with volume 1,728 cubic inches
6. A cube with volume 648 cubic inches
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7. What is the volume of a cube with a side length of 8 inches?
8. What is the volume of a cube with a side whose diagonal
2 inches?
measures 5 √#
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page 2
In 9–13, find the distance between the given points. Give the exact
simplified value.
9. (2, 6) and (7, 1)
10. (5, −7) and (8, 2)
11. (10, −12) and (9, −14)
12. (−7, −8) and (1, 2)
13. (−9, −9) and (−11, 5)
y
14. Use the graph at the right to complete the following.
5
4
3
2
1
5 4 3 2 1
1
B (2, 1)
x
1 2 3 4 5
C (5, 2)
A
(1, 2) 3
4
5
D (2, 5)
a. What is the exact value of the distance between A and B?
b. What is the exact value of the distance between C and D?
c. What is the exact value of the perimeter of the rectangle?
15. Use the graph below to complete the following.
5 4
2 1
1
Y
(3, 2)
3
4
5
x
1
3 4 5
Z (5, 2)
a. What is the exact value of the distance between X and Z ?
b. What is the exact value of the area of △XYZ ?
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y
5
4
X (3, 2) 3
2
1
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8-9A Lesson Master
Questions on SPUR Objectives
See pages 521–523 for objectives.
SKILLS Objective C
In 1–6, rewrite without parentheses and without negative exponents.
5m2n 4
2. _____
3 4
( 4m n )
6m n
4. (_______
11m n )
1. (2a 3b−4)3
−1 2
3. (−7x −4y 8) · (2x 5y)6
−2
4 −7
5. (6x 3y −6)−2
6. (−a 4b 2)−3 · (2a5b−6)
PROPERTIES Objective F
7. Tell whether the pattern 3x 2 = x 3 is true for the given instances.
b. x = 1
a. x = 0
c. x = 3
_1
8. Tell whether the pattern x 2 = √$x is true for the given instances.
a. x = 0
b. x = 1
c. x = 4
9. Find a counterexample for the pattern x 2 · x 4 = x 8.
3a7b2 −2
10. Terri and Kandy both simplified ____
. State which property
a5b−6
( )
each student used for each step of their work.
Terri’s Work
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Step 1: (3a2b8)−2
a.
Step 2: 3−2a−4b−16
b.
1
Step 3: _____
4 16
c.
9a b
Kandy’s Work
(3a7b2)−2
(a b )
Step 1: _______
5 −6 −2
−2 −14 −4
d.
3 a b
Step 2: ________
−10 12
e.
Step 3: 3−2a−4b−16
f.
1
Step 4: _____
4 16
g.
a b
9a b
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