Download 2 - haiku learning

More Multiplication Properties
of Exponents
California Content Standards
2.0 Understand and use the rules of exponents. Develop
10.0 Multiply monomials. Solve multi-step problems, including word problems, by using this
technique . Develop
What You'll Learn
• To raise a power
to a power
Lesson 7-3
Rewrite each expression using each base only once.
1. 3 2 •
3. 5 7 .
• To raise a product
to a power
... And Why
for Help
@ Check Skills You'll Need
2. 2 3 • 2 3 . 2 3 . 2 3
32 • 32
5 7 . 57 . 5 7
4. 7 . 7 . 7
Simplify.
6. a 2 • a 2 • a2
5. x 3 • x 3
7. y-2 . y-2 . y-2
To find the resting energy of an
object, as in Example 5
8. n - 3
•
n- 3
r -. - ·-- - - · -----·. -·------- -- ----------------------------------
Raising a Power to a Power
CA Standards
Investigation
nline ~
active math ·.
Powers of Powers
You can use what you learned in the previous lesson to find a shortcut for
simplifying expressions with powers. Copy and complete each statement.
1. (3 6)2 = 3 6 . 3 6 = 3
2. (5 4)3
=
= 36 .
+
5 4 · 5 4 · 5 4 = 5-' + u +
3. (27)4 = 27 . 27 . 27 . 27 = 2u +
For: Exponent Activity
Use: Interactive Textbook, 7-4
4. (a 3)2
5.
= a3 • a3 =
aL + •
(g 4)3 = g 4 . g 4 . g 4 = g
6. (c 3) 4
= 3
= 5 4 · • = 5•
+
+.
= 27 . • = 2.
= a3 · • = a
+ u + .... = g 4 . .... = g .
= c 3 • c 3 · c 3 • c3 = c
+
+
+
= c3.
c
7. a. Make a Conjecture What pattern do you see in your answers to
Questions 1- 6?
b. Use your pattern to simplify (8 6)3.
Raising a power to a power is the same as raising the base to the
product of the exponents.
Property
Raising a Power to a Power
For every nonzero number a and integers m and n, (am)n = amn.
Examples (54)2 = 54 ·
2
= 58
Lesson 7-4
(x2)5 =
x2 · 5
= xlO
More Multiplication Properties of Exponents
345
Simplifying a Power Raised to a Power
Simplify (x 3)6.
(x 3)6 = x 3 · 6
=
@CA Standards Check
Multiply exponents when raising a power to a power.
x 18
Simplify.
G) Simplify (a 4 ) 7 and (a - 4 ) 7 .
Be sure to use the order of operations. Simplify expressions in parentheses first.
. . Simplifying an Expression With Powers
Simplify c 5(c 3 ) -
2.
c 5(c3) - 2 = c 5 · c 3 · (- 2)
Multiply exponents in (c 3) - 2.
= c 5 • c- 6
Video Tutor Help
=
Visit: PHSchool.com
Web Code: bae-0775
c5
= c-
+ (-
Simplify.
6)
Add exponents when multiplying powers with the same base.
1
Simplify.
= ~
@CA Standards Check
Write using only positive exponents.
Q) Simplify each expression.
,-·Raising a
P~roduct
a. t 2(t 7)-2
b. (a4)2 .
(a2)5
to a Power
You can use repeated multiplication to simplify expressions like (5y) 3.
(5y) 3 = 5y . 5y . 5y
=5·5·5·y·y·y
= s3y3
= 125y 3
Notice that (5y) 3 = 53y 3. This illustrates another property of exponents.
Property
Raising a Product to a Power
For every nonzero number a and band integer n, (ab )n = anbn.
(3x) 4 = 3 4x 4 = 81x 4
Example
Simplifying a Product Raised to a Power
Simplify (2x 4)2.
When raising a product to a
power, make sure each factor
of the product is raised to the
power.
(2x4)2 = 2 2(x4)2
=
~
=
22x8
4x
8
Raise each factor to the 2nd power.
Multiply exponents of a power raised to a power.
Simplify.
e The correct answer is D.
@CA Standards Check ® Simplify each expression.
346
Chapter 7 Exponents
a. (2z ) 4
b. (4g5)-2
l
J
Some expressions have more than one power raised to a power.
_ Simplifying a Product Raised to a Power
Simplify (x - 2)2(3xy 2)4.
(x -2)2(3xy2)4 = (x -2)2 . 3 4x 4(y2)4
=
@CA Standards Check
,,,,,,
,
_.
L'
Use the Commutative Property of Multiplication.
= 3 4x 0y8
= 81y 8
Add exponents of powers with the same base.
Simplify.
c. (6mn) 3(5m-3)2
b. (2a 3 )5 (3ab 2 )3
(c 2 )3 (3c 5 ) 4
--.···----...·-·--·-··-
'
01 I
= 34 • x - 4 . x 4 . y8
You can use the property of raising a product to a power to solve problems
involving scientific notation. For an expression like (3 X 10 8)2, raise both 3 and 10 8
to the second power.
{r~
,·... ,·,_,,,;.'·.·,.
.. ~"'.
Multiply the exponents of a power raised
to a power.
x - 4 . 3 4x4y8
4} Simplify each expression.
a.
'
Raise the three factors to the 4th power.
EXAMPLE
.
' ,••\
"
Application
All objects, even resting ones, contain energy. A raisin has a mass of 10 - 3 kg.
The expression 10 - 3 • (3 X 10 8)2 describes the amount of resting energy, in joules,
the raisin contains. Simplify the expression.
10- 3 · (3
x 10 8)2 =
Albert Einstein is famous for
discovering that the amount
of energy in an object,
measured in joules, is equal
to its mass in kg multiplied by
(3 x 10 8 m/s) 2 .
10- 3 . 32 . (1o8) 2
= 10- 3 • 32 · 10 16
= 32 •
10 - 3
•
= 32 • 10 -3 +
Simplify ( 108) 2.
10 16
Use the Commutative Property of
Multiplication.
16
Add exponents of powers with the
same base.
= 9 x 10 13
@CA Standards Check ® a. The mass of a feather is 10-
Raise each factor within parentheses to the
second power.
Simplify. Write in scientific notation.
Simplify the expression (10 - 5 )(3 x 108)2 to
find the amount of resting energy in joules the feather contains.
b. The mass of a drop of water is 2.5 X 10- 2 kg. Simplify the expression
(2.5 X 10- 2)(3 X 108)2 to find the amount of resting energy in joules the drop
of water contains.
5 kg.
For more exercises, see Extra Skills and Word Problem Practice.
Sc&£5.2
0
Practice by Example
Examples 1, 2
for
Help
(page 346)
Simplify each expression.
1. (c5)2
2. (c2)5
5. (c5)3c4
6.
3.
(d3)5(d3)0
Lesson 7-4
(n8)4
7. (t2) -2(t2) -5
4. (q10)10
8. (x3) -1(x2)5
More Multiplication Properties of Exponents
347
Example 3
(page 346)
Simplify each expression.
9. (5y) 4
10. (4m) 5
11. (7a) 2
12. (12g4)- 1
13. (6y 2)2
14. (3n 6)4
15. (2y 4)- 3
16. (2p 6 ) 0
Example 4
17. (x 2)5(x 3)2
18. (2xy ) 3x 2
19. (mg 4)- 1(mg 4)
(page 347)
20. (c- 2)3c- 12
21. (3b - 2)2(a 2b 4)3
22. (2a2c4) - 5(c- 1a7)6
Example 5
(page 347)
Simplify. Write each answer in scientific notation.
23. (4 X 10 5 ) 2
27.
(7
X 10 4 )2
24. (3 X 105)2
zs. (2 x 1o- 10p
26. (2
28. (6 X 1012)2
29. (4 X 108)-2
30. (3.5 x 1o- 4)3
x 1o-3)3
31. The length of one side of a cube is 9.5 X 10- 4 m. What is the volume of
the cube?
0
Apply Your Skills
Complete each equation.
(x 2) = x6
35. (y-4) = y12
33.
(m )3
= m - 12
34. (b 2)
36.
(n 9 )
= 1
37. 7(c1)
38. (5x )2 = 25x - 4
39. (3x 3y )3 = 27x 9
32.
40.
=
b8
= 7c 8
1(m 2n3 ) = -m6n9
~
41. Error Analysis One student simplified x 5 + x 5 to x 10 . A second student
simplified x 5 + x 5 to 2x 5. Which student is correct? Explain.
t
Simplify each expression.
42. (4.1) 5 . (4.1) - 5
43. 32(3x) 3
44. (b5)3b2
45. ( -5x) 2
46. (2x - 3)2 · (0.2x) 2
47. ( -2a 2b )3(ab )3
49. (1o 3)4(4.3 x 1o-8)
SO. (4xy 2)4( -y) - 3
48.
+
5x 2
(3 7 )2 . (3- 4) 3
51. a. Write an expression for the surface area of
each cube.
b. How many times greater than the surface
area of the small cube is the surface area of
the large cube?
c. Write an expression for the volume of
each cube.
d. How many times greater than the volume of
the small cube is the volume of the large cube?
/
~
~
2x
4x
Write each expression with only one exponent. Use parentheses.
52. m 4 • n 4
53. (a 5)(b 5)(a 0)
54. 49x 2y 2z 2
2
55. 12 _x;
3y
56. Choose a value of n for the expression an. Express the power you wrote as a
product of the form (ac)d in four different ways.
Homework Video Tutor
......
lW
.,.,.,.
"'
__)
Visit: PHSchool.com
Web Code: bae-0704
348
Chapter 7
Exponents
57. Write each answer as a power of 10.
a. How many cubic centimeters are in a cubic meter?
b. How many cubic millimeters are in a cubic meter?
c. How many cubic meters are in a cubic kilometer?
d. How many cubic millimeters are in a cubic kilometer?
58. Write each answer as a power of 2.
a. Computer capacity is often measured in bits and bytes. A bit is the smallest
unit, a 1 or 0 in the computer's memory. A byte is 23 bits. A megabyte (MB)
is 2 20 bytes. How many bits are in a megabyte?
b. A gigabyte (GB) is 210 megabytes. How many bytes are there in a gigabyte?
How many bits are there in a gigabyte?
59. a. Earth has a radius of about 6.4 X 10 6 m. Approximate the surface area of
Earth using the formula for the surface area of a sphere, S = 4.nr 2 .
b. Earth's surface is about 70% water, almost all of it in oceans. About how
many square meters of Earth's surface are covered with water?
c. The oceans have an average depth of 3795 m. Estimate the volume of water
on Earth.
60. Which expression or expressions do not equal 64?
A. 25 · 2
E. (22)(22)2
D. (2 3) 2
C.2 2 • 23
B. 2 6
61. Writing Explain how you know when to add the exponents of powers and
when to multiply the exponents.
Challenge
Solve each equation.
Sample
25 3 = 5x
(5 2)3 = 5x
56
= 5x
6 = x
Write 25 as a power of 5.
Simplify (5 2)3.
Since the bases are the same, the exponents are equal.
62. 56 = 25x
63. 82 = 2x
64. 3x = 27 4
65. 4x = 2 6
66. 32x = 94
67. 2x =
l2
34
68. Critical Thinking Simplify (x 3) 4 and x . Are the expressions equivalent?
- ~-M
·r _"T -·~
!t,· ··-·-cli
'P e . -·-p-~
o1ce . rae · •••ce~;::j~:~. )~: . ---For California Standards Tutorials, visit PHSchool.com. Web Code: baq-9045
Alg1 2.0
69. Which expression is equivalent to (x 3y ) 3?
Cl0
Alg1 2.0
Alg118.0
Alg117.0
x3y3
®
x6y3
©
x6y4
®
x 9y3
70. Evaluate 3a2 for a = 5.1 X 10- 5.
®
1.53 x 10- 10
©
7.803 x 10- 10
®
1.53 x 10- 9
®
7.803 x 1o- 9
Cl0 {(2, - 1), (3, -1), (5, - 1), (9, - 1)}
©
{(3, 4),(!,-3), (-2, 4),(-5, 7)}
®
®
{(0,0), (-1, -1), (-2, -3),(1,4)}
71. Which relation is NOT a function?
{(1, 2), (3, 4),(1, 4),(3, 5)}
72. Which solution set describes the range of the function y = - 3x
+ 1 for the
domain {1.5, 1.75, 2, 2.25}?
Cl0 {5.5, 6.25, 7, 7.75}
©
{-7.5, -8.25, -9, -9.75}
®
®
{7.5, 8.25, 9, 9.75}
{-3.5 , -4.25, -5, - 5.75}
nline Lesson Quiz Visit: PHSchool.com, Web Code: baa-0704
349
73. Which graph represents the function rule f(x) = 3x +
~
®
fY
-2
01
C0
I/
2
4 'y
X
®
®
-2
1?
4'y
X
---
- ·-
' '>JVI•xeil Revi.etn.l ·
Lesson 7-3
for
Help
. , ,'.; ....
Simplify each expression.
74. bc - 6 • b
Lesson 6-2
75.
76. 9m 3( 6m 2 n 4 )
77. 2t( -2t 4 )
80. y
81. y =X+ 4
Solve each system using substitution.
78. y = 3x + 5
y = -4x + 12
Lesson 5-1
(a 2b 3 )(a 6 )
79. y = 0.5x - 1
y = 0.2x + 0.4
=
5x - 9
y = 3x
+5
y = -5
Find the slope of the line that p~sses through each pair of points.
83. (2, -5), (3, 1)
82. (0, 3), ( 4, 0)
84. (- 3, 6) , (1, 0)
85. (0, 0) , (11 , -9)
Find the slope of each line.
86.
87.
4'y
-2
-2
O+
2
X
X
1. m- 3n°m 1
2. 5c2 · 7c-2
3. a3b · a-6b-2
4. -3,2 · 2- 6 · r- 7
5. (p4)2(p0)9
6. (a-3) - 2
7. (25) - 1(3b) 3
8. (c2d-2)3
9. In 2000, about 1.4 X 104 ships passed through the Panama Canal. About
5.2 X 107 gallons of water flow out of the canal with each ship. About how
many gallons of water flowed out of the canal with the ships in 2000? Write
your answer in scientific notation.
10. The moon has a radius of about 1.7 X 106 km.
a. Approximate the surface area of the moon using the formulaS= 4nr2 .
b. Approximate the volume of the moon using the formula V = ~nr 3 .
350
Chapter 7
Exponents
Division Properties
of Exponents
California Content Standards
2.0 Understand and use the rules of exponents. Develop
10.0 Divide monomials. Solve multi-step problems, including word problems, by using this
technique. Develop
What You'll Learn
• To divide powers with
the same base
@ Check Skills You'll Need
Skills Handbook page 598
Write each fraction in simplest form.
5
1· 20
• To raise a quotient to
a power
2 125
• 25
6
5· 15
.. . And Why
6·
6y2
5xy
9· 15x
To find the amount of paper
recycled per person in the
United States, as in Example 2
,..----·-
8
30
10. 3X
---.
......
-·-----~--·-·
-
60
3· 100
4. 124
7• 10
35
8• 18
63
3ac
11• 12a
12. 24m
4
6mn 2
------------------------------·--·--·-- ................ ,.... __ --------- ··--------- .. -...-·-----_,
Dividing Powers With the Same Base
You can use repeated multiplication to simplify fractions. Expand the numerator
and the denominator using repeated multiplication. Then cancel like terms.
56 52 -
$ . $ . 5 . 5 . 5 . 5 $ . $
-
54
Dividing Powers With the Same Base
m
For every nonzero number a and integers m and n , an = am- n.
Example
31
33
=
37 - 3
=
a
34
Since division by zero is undefined, assume that no base is equal to zero.
Simplifying an Algebraic Expression
Simplify each expression.
a. a 6 =a 6-14
14
a
= a -8
Simplify the exponents.
-
Rewrite using positive exponents.
1
- a8
Video Tutor Help
Visit: PHSchool.com
Web Code: bae-0775
Subtract exponents when dividing powers
with the same base.
1 3
b • c 5- d-4 = c -1- 5d 3- (-4)
c d
= c -6d 7
d7
=6
c
Subtract exponents when dividing powers
with the same base.
Simplify.
Rewrite using positive exponents.
Lesson 7-5
Division Properties of Exponents
351
~ Simplify each expression.
{iJ CA Standards Check
zlO
b4
a2b
b. s
a.9
z
b
d. m - ln2
m 3n
c. a4b3
e.
x2y-l
4
z
xy4z-3
When you divide numbers that are in scientific notation, you can use the property
of dividing powers with the same base. In real-world situations, decide whether to
write the result in standard or scientific notation.
Application
In 2000, the total amount of paper and paperboard recycled in the United States was
37 million tons. The population of the United States in 2000 was 281.4 million. On
average, how much paper and paperboard did each person recycle?
37 million tons
_
3.7 X 10 7 tons
281.4 million people - 2.814 x 10 8 people
3.7
= 2.814 X 10 7 - 8
California generates nearly
1.4 X 107 tons of
postconsumer paper annually.
3.7
- 1
Write in scientific notation.
Subtract exponents when dividing
powers with the same base.
Simplify the exponent.
= 2.814 X 10
= 1.3 x 10- 1
Divide. Round to the nearest tenth.
= 0.13
Write in standard notation.
There was about 0.13 ton of paper and paperboard recycled per person in 2000.
{iJ CA Standards Check
J) Find each quotient. Write each answer in scientific notation.
b 7.5
• 2.5
a 2 X 103
•8
X
10 8
X
X
1012
10- 4
C
•
4.2 X 105
12.6 X 10 2
d. In 2000 the total amount of glass recycled in the United States was 2.7 million
tons. The population of the United States in 2000 was 281.4 million people. On
average, about how many tons of glass were recycled per person?
r··-··r~-
-.,. ----··-·-·""'"
"---~-
Raising a Quotient to a Power
You can use repeated multiplication to simplify the expression
(y)3= ~ . ~ . ~
= x·x·x
y. y. y
- x3
-3
y
This illustrates another property of exponents.
Property
Raising a Quotient to a Power
For every nonzero number a and band integer n,
Example
352
Chapter 7
Exponents
4)3
43
64
( 5 = 53 = 125
(5)n = %~·
(y) 3.
Raising a Quotient to a Power
3
Which expression is equivalent to ( : 2 ) ?
Check your answer when
simplifying by substituting a
value for the variable.
For x = 2,
(~ )3=
(a )3 = 13 = 1
12xs
®
4 )3
43
( x2
= (x2)3
=
64 - 64 - 1
26 - 64 -
1x62
®
!
4
X
©
64
xs
®
64
x6
Raise the numerator and the denominator to the third power.
Multiply the exponents in the denominator.
= 6~
Simplify.
X
The correct answer is D.
{iJCA Standards Check
a. (: 2)2
Q) Simplify each expression.
b.
(;2)3
You can use what you know about exponents to rewrite an expression in the form
using positive exponents.
(z;)-n
(Jitn =
So,
dt
Use the definition of negative exponent.
1
an
bn
1 bn
= an . bn
bn
bn
an
Use the Identity Property of Multiplication to multiply by g~ .
= (~)n
Write the quotient using one exponent.
Raise the quotient to a power.
Simplify.
(5)-n= (~)n.
Simplifying an Exponential Expression
Simplify each expression.
a. (~) -2 = (~) 2
Rewrite using the reciprocal of~-
- 52
- 32
Raise the numerator and denominator to the second power.
= ; or 2~
Simplify.
2
b. (
_2;)-4 = ( -Jx)4
Write the fraction with a negative numerator.
- ( -y)4
- (2x) 4
Raise the numerator and denominator to the fourth power.
_L
Simplify.
® Simplify each expression.
a.
(l)-3
r.
= ( ;~)4
- 16x 4
{iJ CA Standards Check
Rewrite using the reciprocal of -
)-5
b. ( 21
lesson 7-5
c.
(2;)-1
d.
(7,;:)-2
Division Properties of Exponents
353
EXERCISES
For more exercises, see Extra Skills and Word Problem Practice.
Standards Practice
Practice by Example
for
Example 1
--·
Alg1 2.0, 10.0, 2s.o
Copy and complete each equation.
1. 5 ~ = 5
5
(page 351)
Help
·--·--
2. 2 ~ = 2
3. 3 ~ = 3
2
4. 5253
= 5
5352
3
Simplify each expression.
25
27
5. 7
2
10. xl3y2
9. 3s - 9
6s - ll
Example 2
c12
8. m - 2
7. 15
6. 5
2
c
m-5
11 c2d - 3
12. 32m3t6
• c3d - 1
x13y
35m7t - 5
Simplify each quotient. Write each answer in scientific notation.
(page 352)
19. In 2000, people in the United States over age 2 watched television a total of
386 billion hours. The population of the United States over age 2 was about
265 million people.
a. Write each number in scientific notation.
b. Find the average number of hours of TV viewing per person older
than age 2 for 2000.
c. On average, how many hours per day did each person older than
age 2 watch television in 2000?
20. The speed of computers is measured in number of calculations per picosecond.
There are 3.6 X 1015 picoseconds per hour. What fraction of a second is a
picosecond?
Example 3
Simplify each expression.
21.
(~?
22.
(i)3
25.
(~2)3
26.
(~!) 2
(page 353)
Example 4
29. (~) -
1
30. (~) -
(page 353)
33.
Apply Your Skills
(31~t)2
34. (
(2;)5
2
27. (:6 )
23.
2
31. ( -~) -
4~ )3
35.
2n2
2
(~~) 3
24.
(ig )4
28.
(2t)3
32. ( -~) 36.
Explain why each expression is not in simplest form.
37. 5 3m 3
38. x 5y - 2
39. (2c)
4
3
(3~2)o
d7
40. x 0y
41.{[
Simplify each expression.
32 .3 so
2
3
46. (iG)
42.
354
Chapter 7
Exponents
43.
(2m5)-4
-2
m
n4n
47. ( ----=2
n
)-4
44.
48.
(2a7)(3a2)
(5x) 3
45.
2k32)-2
(3k-
49 ~10)2
Sx3
6a 3
. 77
50. At the end of 2003, there were about 158.7 million wireless telephone
subscribers in the United States. These subscribers matle about 23.7 billion calls
and used about 80.5 billion minutes per month.
a. Write each number in scientific notation.
b. What was the average number of minutes used by each subscriber per
month? Round to the nearest whole number.
c. What was the average length of a phone call? Round to the nearest tenth.
4
In 2003, about 2.0 X 107
people in California had cell
phones.
51. a. Writing While simplifying the expression ~,
.
c
Kneale smd, "I've found a property of
exponents that's not in my algebra book! "
Write an explanation of why Kneale's
method works.
b. Apply Kneale 's method to an example
you create.
Simplify each expression.
2ab6)-2
52. ( -3ab
56.
53.
a3b2c- 4
-2 5 a b c
57.(a)
(-2t4
2
(p-2q4r)5
p3q5
54.
Kneale
c;4
1
c6 = c;6-4 = c;2
(13 )- 3
(*)-2
58. ( (3x) 2
x2/
55. 0.22 • 0.23
0.26
y)-2
59.
(5a2X6b3)
(2a 3X25b-2)
60. The area of the rectangle is 60a 2b5.
What is the width of the rectangle?
® a2 b5
© _5_
5
a2b5
®
5ab 4
®
12ab
5a 3b 6
61. Critical Thinking Lena and Jared used different methods to simplify ( ~) 2 .
Why are both methods correct?
b
Lena
Jared
(!;r =
b6
=
b8
b14
(!;r =
=
(b4)2
b8
62. a. In 2000, the United States government owed $5.67 trillion to its creditors.
The population of the United States was 282.2 million people. How much
did the government owe per person in 2000? Round to the nearest dollar.
b. In 2005 the debt had grown to $7.93 trillion, with a population of 296.4 million.
How much did the government owe per person? Round to the nearest dollar.
c. What was the percent of increase in the average amount owed per person
from 2000 to 2005?
Visit: PHSchool.com
Web Code: bae-0705
63. a. Error Analysis What error did the student
make in simplifying the expression at
the right?
b. What is the correct answer?
=1
Lesson 7-5
Division Properties of Exponents
355
Write each expression with only one exponent. You may need to use parentheses.
35
5
67. 107 . 100
d8
d
m7
64. 5
65. 7
66. 5
68. 27x3
8y3
69. 4m2
70. 49m2
25n 2
n
169m4
10- 3
71. 125c7
216c 4
72. If you donate blood regularly, the American Red Cross recommends a 56-day
waiting period between donations. One pint of blood contains about 2.4 X 10 12
red blood cells. Your body normally produces about 2 X 10 6 red blood cells
per second.
a. At its normal rate, in how many seconds will your body replace the red
blood cells lost by giving one pint of blood?
b. Convert your answer from part (a) to days.
73. a. Write three numbers in scientific notation.
b. Divide each number by 2.
c. Critical Thinking Is the power of 10 divided by 2 when you divide a number
in scientific notation by 2? Explain.
a
Math Reasoning Which property o r properties of exponents would you use to
simplify each expression?
22
78. (24)3
1
74. 2- 3
75.5
76. (~Y
77. 2-427
215
2
Challenge
Simplify each expression.
79. nx +
2 -:-- nx
80. n Sx -:-- nx
81.
(~)2
xm - 2
82.
(~!)
n3
83. The ratio of a planet's maximum to minimum distance from the sun is related
to how circular its orbit is.
a. Copy and complete the table below. Round decimals to the
nearest hundredth.
b. Reasoning How can you use the ratio maximum :minimum to determine
whether a planet's orbit is close to circular?
c. Which planet has the least circular orbit? The most circular orbit?
Distance From the Sun
(kilometers)
3 56
Chapter 7
Exponents
Planet
Maximum
Minimum
Maximum : Minimum
Mercury
6.97 X 107
4.59 X 107
• :•=
Venus
1.089 X 108
1.075 X 108
1.089 X 108 :
Earth
1.521 X 108
1.471 X 108
J : 1.471 X 108 = t
Mars
2.491 X 108
2.067 X 108
-.
=
Jupiter
8.157 X 108
7.409 X 108
I ·
=
Saturn
1.507 X 109
1.347 X 109
..J :
=
=
7
6.97 X 10
4.59 X 107
~
Uranus
3.004 X 109
2.735 X 109
-
Neptune
4.537 X 109
4.457 X 109
J:
~
.
=
=
=
6.97 = 1.52
4.59
~...IVI~ItipiF"Ciioice-Practice
For California Standards Tutorials, visit PHSchool.com. Web Code: baq-9045
Alg1 2.0
32 -3 ) - 2
84. Which expression is equivalent to ( : 2
?
3
®
-5
® j_5
©
Alg1 7.0
Alg1 2.0
slO
9
3s
85. Look at the line shown on the graph. What is the equation of the line with half
the slope and the same y-intercept?
®
y =
-~x + 2
©
®
y = -~x + 3
®
-~x + 2
y =
-ix + 3
y =
2
86. Which expression is NOT equivalent to ( 4n 5 ) - ?
.
®
Alg1 5.0
®
_l_3
s
3m
®
(3m5) 2
~
4n -2
~
©
®
9m10
1~
(16n2)- 1
9m10
87. A radio station is organizing a fundraiser to build a new public library. The
radio station will donate $.50 for every dollar donated by the listeners. If the
listeners donated $530 on the first day of the fundraiser, how much did the
radio station donate on the first day?
® $106
®
$265
© $1060
® $2650
,<f;·'!JJVIixeil ' Review
for
Help
Lesson 7-4
Simplify each expression.
88. (3y 2 )3
91. 2(3s- 2 ) -
89.
3
94. (70n -3)2(n5)2
Lesson 6-1
90. (r2t- 5) - 4
92. (23c2) -1
93. ( -3)2( -r3)2
95. (72y12)0
96.
(5x3)2
Solve each system by graphing.
97. y = 3x
y = -2x
Lesson 4-5
(2m- 7)3
98. y = 2x + 1
y=x-3
99. y = 5
100. y = 7
3
y=8
X=
Write an equation of the direct variation that includes the given point.
101.(3,8)
102. ( -5, 2)
103. (6, - 7)
104. ( -3, - 5)
105. (4, 7)
106. ( - 16, 4)
107. (9,5)
108. (4,-2)
109. (7,1)
nline Lesson Quiz Visit: PH SchooL com, Web Code: baa-0705
357
2.0 Understand and
use the rules of
exponents. Develop
Understanding Word Problems Read the exercise below and then follow along
with what Casey thinks and writes. Check your understanding with the exercise
at the bottom of the page.
If you donate blood regularly, the American Red Cross recommends a 56-day waiting
period between donations. One pint of blood contains about 2.4 X 1012 red blood cells
(RBCs). Your body normally produces about 2 X 106 red blood cells per second.
a. At its normal rate, in how many seconds will your body replace the red blood cells
lost by giving one pint of blood?
b. Convert your answer from part (a) to days.
What Casev fhittks
First, I'll read the problem and write down the
important information.
What Casev Writes
...,.
To answer part (a) , I'll write an equation relating
the information in the problem.
1pitrt of blood cotrtaitts 2.4 x totz RJCs.
Jody produces 2 x t06 RJCs per secottd.
Nutttber of RJCs produced =
rate body produces RJCs x tittte
f
Since I need to find out how many seconds it
will take to replace the RBCs, I'll solve this
equation for time by dividing each side of the
equation by the rate.
Now I'll substitute the information from the
problem into my equation and simplify.
_ t1Utttber of RJCs produced
lttte - rate body produces RJCs
. t.4 x totz t.4 tz - 6
rrttte = t x to6 = T x 10
= 1.2 x 106 secottds
60 sec;ot1ds
tttrt1ute
x
60 tttit1utes x 24 hour =
hour
day
86 ~0 secot1ds = 8 64
'
To answer part (b) , I need to find out how many
days there are in 1.2 X 106 seconds. First, I will
find out how many seconds there are in one day.
1.! X 106
8.64 x
Hair growth rates differ among people. Suppose your hair grows at a rate of
3.2 X 10- 4 m per day. About how many days will it take for your hair to grow
3.5 x 10- 1 m? About how many years is this?
Guided Problem Solving
Understanding Word Problems
X
104
1.!
tOZ = 1S.9 days
It will take about 1.2 x 106 secottds, or
1S.9 days, to replace the red blood cells lost
itt 1 pitrt of blood.
EXERCISE
358
•
to-+= 8.64 x to6- 4 =
0.1S9 x
Now I will divide my answer to part (a) by the
number of seconds in a day. I'll write my answer
in a sentence.
day
There are many rules of exponents in this chapter. To remember these rules, it may
help you to make a flash card.
Follow the steps below to make a card for the rule Zero as an Exponent.
1. Write the name of the rule.
2. D escribe the rule in words.
3. Give an arithmetic example of the rule.
4. Give an algebraic example of the rule.
Zero as an Exponent
Word description: Any number other than
zero raised to the zero exponent equals 1.
Arithmetic
5°= 1
Algebra
For every nonzero
number a, a 0
1.
=
EXERCISES
Follow the steps above to make a card for each rule of exponents.
1. Negative Exponent
2. Multiplying Powers With the Same Base
3. R aising a Power to a Power
4. Dividing Powers With the Same Base
5. R aising a Quotient to a Power
6. Error Analysis A student made a card for the rule R aising a Product to a Power.
Which parts are incorrect? Explain.
Raising a Product to a Power
Word description: A product raised to a power equals
the product of each factor raised to that power.
Arithmetic
(2x) 6
=
2x 6
Algebra
For every number a, b, and n,
(ab)n
anbn.
=
Vocabulary Builder
Remembering Properti es
359
One advantage of multiple-choice tests is that the correct answer is always among
the choices. A strategy is to work backward by taking answers and testing them in
the original problem.
Which is always a correct conclusion about the quantities in the function
y=2x-1?
CJD The variable y is always 1less than x .
®
©
®
As the value of x increases, the value of y decreases.
The variable y is always greater than x.
When the value of x is negative, the value of y is also negative.
When testing statements, testing a single value or case is often not enough.
In this case, making a table of values for the function
y = 2x - 1 will make it easier to test all the statements.
Choice A: When x = 0, y is 1less than x. However, this is not true
for any other number in the table, so A is not correct.
X
2x-1
y
-2
2( - 2)-1
-5
-1
2( -1)-1
-3
Choice B: The table shows that as the x-values increase from -2
to 2, they-values increase from -5 to 3. SoB is not
correct.
0
2(0)-1
-1
1
2(1)-1
1
Choice C: When x = 2, y is greater than x. For all the other values
in the table, y is less than or equal to x. SoC is not correct.
2
2(2)-1
3
Choice D: For every negative x-value in the table, y is negative. Since 2 times a
negative number is always negative, and a negative number minus 1 is
always negative, D is always true.
1. Marie recorded the number of pages she read in her history
book and the amount of time it took in the table at the right.
Which equation best represents the relationship between the
number of pages p and the amount of time t?
ClD t = p + 16
•
®
t=3p
~
~
t-E
-3
@
t=p 2
-40
p
Time, t
(minutes)
8
24
12
36
14
42
19
57
Pages Read,
2. Which statement is always a correct conclusion about the quantities in the function y = 2x?
CJD
®
©
®
360
The value of y is always twice the value of x.
When the value of x is negative, the value of y is negative.
When the value of xis a positive integer, y is an odd number.
As the value of x increases, the value of y decreases.
Test-Taking Strategies
Testing Multiple Choices
Chapter 7 Review
----·---
rvoca6ulary Review
. >):» English and Spanish Audio
On.lin~
scientific notation (p. 334)
eGo
nline
PHSchool.com
For: Vocabulary qu iz
Web Code: baj-0751
Choose the correct term to complete each sentence.
1. (Scientific notation, Standard notation) is a shorthand way to write very large
and very small numbers.
2. In the expression 84, the (power, exponent) 4 shows that 8 is used as a factor
fo ur times.
· ·- - -·- . . . . . . . ---.... ·-- -·
~-·· sliills·-anii -C:oiice-p·ts-·
Lesson 7-1
• To simpl ify expressions with
zero and negative
exponents (p. 328)
• To evaluate exponential
expressions (p. 330)
Alg1 2.0
--···--·----..·---------·· ---··--.. . . "·· ·------
You can use zero and negative integers as exponents. For every nonzero number a,
a0 = 1. For every nonzero number a and any integer n , a- n = 1n . You cannot use 0
a
as a base. Both 0° and o-nare undefined.
Copy and complete each equation.
3. 1 3a• -
a2
3
x··
1
· 9y• = 9x 6/
4. 4 n;..• = 4n 5
n
5
7.
8. 7k-8h3
Simplify each expression.
6. b - 4c0d 6
x -2
y -8
9. - 1
10.
p2q - 4,0
(~) -4
11. ( -2) - 3
12. -2- 3
13. 7- 2y - 4
14. 9w - 4
-2 7
X y
15. s -2m0
16. 8g- 3h0k6
17. ~
4 -2 3
m - 6nll
X
Evaluate each expression for p
= 2, q = -
19. ( - p) 2q - 2
20. pqqp
18. p2q2
3, and r
y -
= 0.
22. -p2q3
21. p'q'
23. Copy and complete the table below.
2" -
4
•
8
1
-4
•
'2~· ·
0
2
!;;
0
!
-
;-•
24. Which expression has the greatest value for a = 4, b = -3, and c = 0?
A. ab
B.
be
C. b ~a
D. %~
E. ~b
a
25. Critical Thinking Is (- 3b ) 4 = -12b 4? Explain why or why not.
Chapter 7
Chapter Review
361
Lesson 7-2
• To write numbers in
scientific and standard
notation (p. 334)
• To use scientific notation
(p. 335}
~ Alg1 2.0
You can use scientific notation to express very large or very small numbers.
A number is in scientific notation if it is in the form a X 10n, where 1 ~ a < 10,
and n is an integer.
Is each number written in scientific notation? If not, explain.
26. 950 X 10 5
27. 72.35 X 10 8
28. 1.6 X 10- 6
29. o.84 x 1o-5
30. 0.12 X 102
31. 5.471 x 10- 1
32. 10 X 1013
33. 0.71 x.-lo- 6
34. The space probe Voyager 2 traveled 2,793,000 miles. Write the number of miles
in scientific notation.
35. There are 189 million passenger cars and trucks in use in the United States.
Write the number of passenger cars and trucks using scientific notation.
Order the numbers in each list from least to greatest.
36. 7- 2, 7 12 ,7°,7 - 4 , 76,7 1
37. 3.1 X 102,30 X 10-1, 0.3 X 104 ,300 X 10- 4
38. 6.73 X 102,0.6 X 103 ,60.8 X 101,5.6 X 103
39. 100 x 1o- 4 , s x 1o- 3 , so x 1o- 2, 1so x 10- 3
Simplify. Write each answer using scientific notation.
40. 11(3 X 1012)
Lesson 7-3
42. 1.4(1.4 X 10- 3 )
To multiply powers with the same base, add the exponents.
• To multiply powers
(p. 339)
am. an= am+ n
• To work with scientific
notation (p. 340)
Alg1 2.0, 10.0
41. 0.2(7.5 X 10- 2)
Simplify each expression.
43. a2a- 4
44.
t?sF
45. 4x 6 · x- 1
46. n 1 · n 5 · n- 3
47. 4p. p 8
48. (a 4b )(2b 5 )
49. (rs2 )(r8s4 )
50. 11x(4xy- 3)(y 7)
51. w 4 · q · w10
52. ( 4v2 )(5z 9)(12v - 3)
53. -2a2 · ( -Sn)- 2 · 13a6
54. ( -2c10)(bc9)(b5c- 18)
Simplify each expression. Write each answer in scientific notation.
55. (2 X 101)(6 X 104)
56. (7 X 10- 7 )(3 X 106)
57. (11 X 103)(2 X 105)
58. (0.5 X 104 )( 4 X 10-2)
60. (5 X 105)(2.7 X 10-6)
59. (1.2 X 10- 3)(0.6 X 10- 2)
Complete each equation.
61. 42 . 4· = 411
62. 12- 1 . 12· = 123
63. 3• . 35 = 32
64. a- 5 · an = a- 7
65. v2 · v2 · v• = v7
66. rs• · r• = r4s- 3
67. Each square inch of your body has about 6.5 X 10 2 pores. Suppose the back of
your hand has an area of about 0.12 X 10 2 in. 2. About how many pores are on
the back of your hand?
362
Chapter 7
Chapter Review
Lesson 7-4
To raise a power to a power, multiply the exponents.
• To raise a power to a power
(p. 345)
• To raise a product to a
power (p. 346)
(am)n = amn
To raise a product to a power, raise each factor in the product to the power.
(ab)n = anbn
Alg1 2.0, 10.0
Simplify each expression.
68. (m 2) 6
69. (b 7) - 4
70. (h - 1) 3
71. (6y 3) 4
72. (10h7)-1
73. (5x 0 ) 2
74. (2d 2 ) 3
75.
77. ( 1.342 )\1.34) -8
78. (12x 2y -2)5(4xy -3 )-8
76. (5c- 4 )( -4m 8 )2
(q 3 r) 4
79. ( -2r- 4 )2( -3r 2z8)-1
Simplify each expression. Write each answer in scientific notation.
80. (3 X 104 ) 2
81. ( 4 X 10- 5 ) 2
82. (2 X 107 ) 3
83. (103 ) 2 (2 X 10- 4 )
84. (1.5- 2) 2 (1.5 X 101 )2
85. (0.6 X 10- 1) 3
86. Rewrite the expression 27x3y 3 with only one exponent.
87. Write and solve a problem that involves multiplying exponents.
Lesson 7-5
To divide powers with the same base, subtract the exponents.
• To divide powers with the
same base (p. 351)
• To raise a quotient to a
power (p. 352)
S
am
an =a
m - n
To raise a quotient to a power, raise the dividend and the divisor to the power.
an
_
(Q)n
b
- bn
Alg1 2.Q, 10.0
Copy and complete each equation.
65
= 6.
63
88.
-2
74791. 7-274
89.
9-2 = 9.
90. -5
112
= 11.
11 7
9
•
= 7.
92. 3 8 = 32
3
93.
444~
=
4-
48
)
Simplify each expression.
3)·s- 5
w~
95. ( s
98. e -~c3
99. [;
94.
w
(b5)2
e
102.
(xy)-1
x6
103.
(4~-2) -
2
96.
(2~~3)
100.
(3a4
)0
n
97.
(~~r
25
t
s6t-7
101. s-
-3
104. 6d2g7
105.
dg-5
(v2~5
y
Simplify each quotient. Give your answer in scientific notation.
106. 4.2
2.1
X
X
108
10 11
107. 3.1 X 10 4
12.4 X 10 2
108. 4.5
9
109. 5.1
X 103
7
X 10
1.7
8
110. Writing List the steps that you would use to simplify ( 5a 6) -
lOa
Chapter 7
3
X
X
105
10 2
•
Chapter Review
363
n}ine
eGo
Simplify each expression.
r3r-7
1.-5-
2.
t
t - 8m2
(~)-4
3. ---=3
m
4. c 3 v 9c- 1c0
5. h 2 k- 5 d 3 k 2
6. 9y4j2y-9
7. (w2k0p-5)-7
8. 2y-9h2(2yoh-4)-6
For: Chapter Test
Web Code: baa-0752
PHSchool.com
29. Which answer has the numbers listed from least to
greatest?
A. 50 X 10- 2,15 X 10- 1,105 X 10- 2
B. 71 X 102,6.5 X 101,0.08 X 102
C.12 X 102,210 X 10- 1,0.0012 X 10- 3
D. 3.6 X 10°,0.603 X 10 1,6030 X 10- 1
9. (1.2) 5 (1.2) - 2
10. ( -3q - 1)3 q2
Evaluate each expression for a = 5, b = -3, and c = 2.
11. c2.
13.
a3
sb
12. b2
(lc)-3
14. a2 ( -s)- 1c4
16. ( 4c 3 ) 2 ( cb)
15. 2c · ab · 7c
ac
17· ( 2bc
)c
18 2b5
• b4c3
19. (a- 15bc)- 2
20. (0.6)a(0.6)b
21. If n = -3, which expression has the least value?
A. n 2n°
C. nn
B. n 8n-5
D. -nnn- 4
Write each number in scientific notation.
22. There were about 62,041,000 votes cast for George
Bush in the 2004 presidential election.
23. More than 450,000 households in the United States
have reptiles as pets.
Is each number written in scientific notation?
If not, explain.
24. 76 x 10- 9
25. 7.3 X 10 5
26. 4.05 X 10 X 10-8
27. 32.5 X 1013
28. a. The speed of light in a vacuum is about
186,300 mils. Use scientific notation to express
how far light travels in one hour.
b. At its farthest, Saturn is about 1.03 X 109 mi
from Earth. About how many hours does it take
for light to travel from Earth to Saturn?
364
Chapter 7
Chapter Test
30. The length of a rectangle measures 7 d 2 em and the
width measures 32d 5 em. What is the area of the
rectangle?
31. The mass of Mercury is about 3.3 X 1023 kg. A
student made a model of Mercury that weighs 60 g.
Mercury is about how many times larger than the
model?
A. 5.5
X
c.
1024
1.8 x 10- 27
D. 1.8 X 1019
B. 5.5 X 1018
32. Write and solve a problem that involves raising a
power to a power.
33. Which expression does NOT equal32?
A. 2 · 2 4
B. 2(;2 )-
1
D. (2 1 ) 4
C. 2 3 · 22
34. The human body contains about 5 X 106 red blood
cells per microliter of blood, and 3.2 X 104 J.LL
(microliters) of blood for each pound of body
weight. How much does a person with
2.24 X 1013 red blood cells weigh?
Write each expression using only one exponent.
P · 64z 6 · x 4
35. x 2(y 3
3
36. _a_3
125b
37. Lola is putting up a fence around her rectangular
garden that has an area of 35p 3q5 ft 2 . The garden's
length is Sp 2q. What is the garden's width?
38. Folsom Dam in California holds 1 million acre-feet
of water in a reservoir. An acre-foot of water is the
amount of water that covers an acre to the depth of
one foot, or 326,000 gallons. How many gallons are
in the reservoir? Write your answer in scientific
notation.
39. Which expression equals d-3e9j 1 · 14d3 ?
A.O
14~
B. d9f
~
c. 14f
D.
14~
T
Cumulative Practice
Tip 1
Some questions ask you to solve
a problem using exponents. Read
the question at the right. Then
follow the tips to answer the
sample question.
Tip 2
Look for answer choices
that make sense in the
context of the problem.
Think about how the information
given in the problem can be used to
answer the question.
If the side length of a square
can be represented by the
expression 4x2y 6 , which
expression could represent
the area of the square?
®
®
CD
®
~
Think It Through
The side length of the s~uare is 4x2y 6, so
the area is 4x2y 6 X 4x2y . The answer must
contain 4 X 4 = 16. Remember, add the
exponents when multiplying with like
bases. So,x2y6 X x2y6 = x2+2y6+6 = x4yl2.
The correct answer is C.
2xy3
8x4yl2
16X4Y12
l6X4Y36
2. Where is the x-intercept of the line represented by
the equation 8x - 3y = 24? (Lesson 5-3)
CK) x=-8
As you solve problems, you must understand the
meanings of mathematical terms. Choose the
correct term to complete each sentense.
@
x=-3
CD x=3 ®
x=8
3. The data shown in the table at. the
right represent points on a line. What
is the x-intercept of the line?
A. If a line passes through the point (a, 0), then (a, 0)
is called the (x-intercept, y-intercept).
B. A system of linear equations has (infinitely
many solutions, no solution) when the graphs of
(Lesson 5-3)
the equations are parallel.
C. Lines in the same plane that never intersect are
(parallel, perpendicular) lines.
®
(!,o)
CD (2,0)
®
(0, -4)
®
(o,~)
X
y
0
-4
1
4
2
12
3
20
4. If a is positive and b is negative, which
of the following is negative? (Lesson 3-6)
D. A (linear inequality, solution of an inequality)
®
®
describes a region of the coordinate plane that
has a boundary line.
E. The product of two numbers is -1 if one
number is the (multiplicative inverse, negative
reciprocal) of the other.
a+lbl
CD albl
® lal-b
ialb
5. What is the solution of the following system of
equations? (Lesson 6-2)
1
3xy =
4
X+ 3y = 0
Read each question. Then write the letter of the
correct answer on your paper.
1. What is they-intercept of the
function shown on the graph at
the right? (Lesson S-2)
®
(-2,0)
®
(0, -3)
CD ( -~,o)
®
(o,~)
®
(9,-1)
CD (-6,2)
®
(6,-2)
®
(-9,1)
y
6. Which number has the least value? (Lesson 7-2)
2
2
X
®
2.8 x lo-s
®
8.3 x 10- 7
CD 5.3 x 10- 4
® 1.6 x lo- 8
7. Which expression is equivalent to (Pk 3 )(jk2)?
(Lesson 7-3)
®
Pk2
®
Pk5
California Standards Mastery
CD Pk6
®
Pk6
Cumulative Practice
365
Cumulative Practice
(continued)
8. The dimensions of a rectangular
15. Alejandro bought 6 notebooks and 2 binders for
prism are shown in the diagram at
the right. Which expression
represents the volume of the
a2b
rectangular prism? (Lesson 7-3)
®
®
©
®
a2b5
a2b6
ab3
a4b5
ab2
a4b6
3x3y ?
. .
. 1
9 . Which expressiOn IS eqmva ent to ------=2.
3
(Lesson 7-5)
( Y)
®
9x3y3
©
®
27x3y3
®
x3
x3y3
3
is shown in the graph at
the right?
(Lesson 6-1)
3x+ 2y = 6
©
2x + 3y = 12
4 +2
Y -- _lx
®
3x -2y = 12
y = :lx + 2
®
3x + 3y = 9
y = :lx + 2
+2
y = 4x
11. Which statement is true for every solution of the
following system? (Lesson 6-6)
y>x+4
y+x > 4
@
x::S-3 @
x>4 ©
y<5
@
6a 9b5c6
©
®
-27a8b15 c6
- 3abc
®
21
©
44
®
72
14. Mr. Kent sells calculators for $35 each. If an order
is placed from a business account, there is a $50
shipping fee, and no fewer than 100 calculators can
be purchased. Which is a reasonable amount of
money that a business would spend when ordering
calculators? (Lesson 3-5)
® $750 ® $1070 © $2990 ® $3585
366
6n + 3n = 23.52
2b + 4b = 25.53
®
6n + 4b = 23.52
3n + 2b = 25.53
®
9n + 6b = 49.05
n + b = 49.05
®
p = 5s + 20,000
p = s + 32,000
©
p + 0.5s = 20,000
p + 0.1s = 32,000
®
p
p
+ 5s = 20,000
+ s = 32,000
®
p = 0.05s + 20,000
p = 0.01s + 32,000
17. A library is packing its books to move to a new
building. If 4 large and 2 small boxes are used,
124 books can be packed. If 3 large and 5 small
boxes are used, 135 books can be packed. Which
system of equations can be used to find the number
of books s that can be packed in a small box and the
number C in a large box? (Lesson 6-4)
®
C + s = 14
7C + 7s = 259
©
4C + 2s = 124
3C + 5s = 135
®
3C + 4C = 124
+ 5s = 135
2s
4C + 5s = 124
3C + 2s = 135
-27a8b9c6
36 and 48 points on the last quiz. Each question was
worth 2 points, and there was no partial credit.
How many questions could Haley have answered
correctly? (Lesson 3-5)
12
©
y>4
13. All of the students in Haley's class received between
®
6n + 2b = 23.52
3n + 4b = 25.53
®
12. Simplify -3a 8 · cb- 3 · b 12 · 9c5 . (Lesson 7-3)
®
®
®
16. Megan's company pays $20,000 per year plus a
5% sales commission. Laurie's company pays
$32,000 per year plus a 1% sales commission. Which
system of equations can be used to determine the
amount Megan and Laurie must sell s to receive the
same pay p? (Lesson 6-4)
y
10. Which system of equations
®
$23.52. Cassie bought 3 notebooks and 4 binders for
$25.53. Which system of equations can be used to
find the cost of a notebook nand a binder b?
(Lesson 6-4)
California Standards Mastery
Cumulative Practice
18. What is the solution set of the inequality
3l2x - 11 > 15? (Lesson 3-6)
@
x<-2orx > 3
®
x > -2
©
®
-2<x < 3
-3 < x<2
19. Which equation represents a line that is parallel to
y = -:lx + 2? (Lesson 5-5)
®
-y=4x
©
y=4x-12
®
4y + x = 5
®
-:lx - y = -3
20. Which equation represents a line that is
perpendicular to 3y = x and passes through the
point (0, -6)? (Lesson 5-5)
® y = - 3(x + 6)
©
y = 3(x + 6)
®
@
y=3x-6
y=-3x-6
I • for Help to the Lesson in green.
21. Which value below is NOT a solution to the
inequality l6x + 11 ~ 11? (Lesson 3-6)
®
-3
®
-1
CD 2
@
3
22. Which equation represents a line that is
perpendicular to the line shown and passes
through the point shown? (Lesson 5-5)
26. The diameter of Earth is about 1.28 X 104 km.
About what is Earth's radius? (Lesson 7-3)
®
®
2.56
X
108 km
CD 6.4
6.4 x 103 km
®
X
104 km
2.56 x 106 km
27. Which inequality is shown on the graph below?
(Lesson 6-5)
y
6'y
4
,- ,.)If"
2
,. ,.
0
-2
-2
.,. ,. ....
Oj 2
.,I..... .,."""
4
6
X
-2
®
y = -~(x - 6)
®
y
CD y = ~(x - 6) + 3
= -~(x - 6) + 3 ®
y
= ~(x - 6)
23. Which statement is true about the lines shown in
the graph? (Lesson 5-5)
~(x + 1)
CD Y - 1 < ~(x + 1)
+ 1 > ~(x - 1)
® y + 1 < ~(x - 1)
®
y - 1>
®
y
Alg1 2.0
I
6-9, 12, 26
Alg1 3.0
I
4, 18, 21
Alg1 5.0
I
13, 14
Alg1 6.0
-
®
®
The slopes of the lines are the same.
The slopes of the lines are negative reciprocals.
CD The lines have the same y-intercept.
®
The lines have the same x-intercept.
24. Simplify (4m + 7v 2 - v)- (11v- 12m).
(Lesson 1-7)
®
-8m + 7v2 + 10v
2
® 16m +
7v 2
+ 10v
CD 16m+ 7v2 - 12v
® -8m + 7v2 - 12v
Alg1 8.0
I
1-3,27
I
19, 20, 22, 23
Alg1 9.0
I
5, 10, 11, 15-17
Alg110.0
I
24,25
-
-
For additional review and practice, see the
California Standards Review and Practice
Workbook or go online to use
25. Simplify -3x4 · 2y 2 · 4x - 6. (Lesson 7-3)
® 3x- 2y2
® 3x-24y2
CD -24x-2y2
®
_ 24x -24y2
Visit: PHSchool.com, Web Code: baq-9045
California Standards Mastery
Cumulative Practice
367