83. b.Apply the order of operations as follows:

2(3)(6) – ( – 8) = 36 + 8 = 44

84. c.Apply the order of operations as follows:

y= –(– 3)^3 + 3(–3) – 3 = –(–27) –9 – 3 =

27 – 9 – 3 = 15

85. b.Apply the order of operations as follows:

(–5)(6) + (–8)(^12 ) = –30 – 8^12 =

–30 –82 = –30 – 16 = –46

86. b.Apply the order of operations as follows:

^63 ^2 – 4(6) + 10 = ^336 – 4(6) + 10 = 12 – 24 + 10

= –2

87. a.Apply the order of operations as follows:

4(2–2)(2(2)–2)(3( – 2)^2 )=4 ^14  2 ^14 (34) =

=6

88. a.Apply the order of operations as follows:

7(6) + ^162 – (–8) = 42 + 2 + 8 = 52

89. b.Apply the order of operations as follows:

(3(2)(5) + 2)^25 =(32)^25 = ^654 = 12.8

90. d.Apply the order of operations as follows:

 + 

–2

=  + 

• 
  

  2

  
  

^2

7

0 –  2

3

0 –2=  2

4

0 

• 2
  = 
  
  
  • 2
    = 5^2 = 25
  
  
  
  

91. c.Apply the order of operations as follows:

+ = + = + =

+ = =

92. c.Apply the order of operations as follows:

(1)(–1) + –^11 + (1)^2 – (–1)^2 = –1 – 1 + 1 – 1 = –2

93. b.Note that ifx = 2, then y = –2. Now, apply
    the order of operations as follows:
    (((2)(–2)–2)^2 = ((–4)– 2)^2 = (–4)– 2 ^2 = (–4)–4
    = =
    94. b.Apply the order of operations as follows:

^12 [(^62 – 3) – 4(3)] = ^12 [(3 – 3) – 12] = ^12 [–12] = – 6

95. d.Apply the order of operations as follows:

(–8)^2 – 4(3)^2 (^12 ) = 64 – 4(9)(^12 )= 64 – 18 = 46

96. a.Apply the order of operations as follows:

3(6)^2 (–5)(5(3) – 3(–5)) = 3(36)(–5)(15 15)

= 3(36)(–5)(30) = –16,200

Set 7(Page 12)

97. b. = = 33 = 27


98. d.(4w^9 )^3 = 43 w^27 = 64 w^27
    99. b.Note that the power –2 does not apply to the 6
    since it is not enclosed in the parentheses to which
    the exponent applies. Therefore, 6(e– 2)– 2=6e^4.


99. a. (– 45 a^4 b^9 c^5 )( 9 ab^3 c^3 ) = = – 5 a^3 b^6 c^2


100. d. 4 ( 3 x^3 )^2 = 4 ( 32 x^6 ) = 36 x^6


101. d.

4

= 

4

= (a^3 b^2 )^4 = a^12 b^8

103. b. = = = = = xy 5

(^3) 

104. d.^2 ba = ^2 ba^2 ab= ^4 baab= 4


105. c. 3 x^2 y(2x^3 y^2 ) = 6x^5 y^3


106. e.(ab)^2 (ab)–2(^1 a)–1 = =   1 a=


107. c.(3xy^5 )^2 –11x^2 y^2 ( 4 y^4 )^2 = 3^2 x^2 y^10 –
     11 x^2 y^2  42 y^8 = 9 x^2 y^10 – 176x^2 y^10 = 167x^2 y^10


108. a. = = =6x^5 y^3


109. c. = = = =


110. a.“The product of 6x^2 and 4xy^2 is divided by
     3 x^3 y” can be expressed symbolically as ,
     which is simplified as follows:

= = 8^24 x y

(^3) y 2
(6x  3 x (^3) y
(^2) )(4xy (^2) )
 3 x (^3) y
(6x^2 )(4xy^2 )
3 x^3 y
^4
a^2 b^2 x^4
^16 b^2
4 a^2 b^4 x^4
^16 b^2
22 a^2 b^4 x^2 x^2
^42 b^2 x–^2
22 a^2 b^4 x^2
(4b)^2 x–^2
( 2 ab^2 x)^2
^18 x^7 y^5
3 x^2 y^2
2(3^2 x^4 y^2 )(x^3 y^3 )
3 (x^2 y^2 )
2(3x^2 y)^2 (xy)^3
3 (xy)^2
a^5
b^4
a^2
b^2
a^2
b^2
a
1
b–2
a–2
a^2
b^2
a–1
(2b)–1
x^4
y^4 (xy)
xy 44 
xy
xy 22 xy 22 
xy
xy 22 xy––^22
xy
(xy)^2 (xy)–2
xy
a^3 b^3
b
(ab)^3
b
–^45 a^4 b^9 c^5
9 ab^3 c^3
^33 x^6
x^6
^3 x^2 ^3
x^2 x^4
^1
256
^1
(–4)^4
^20
9
^40
18
^16
18
^24
18
^8
9
^24
18
4(2)
3(3)
^6 ^4
2  9
4(2)
3(3)
6(2)^2
2(3)^2
^1
5
^3
10(–2)
^7
5.4
^3
10(–2)
^7
5(–2)^2
^4 ^2 ^3 ^4
4
 4

ANSWERS & EXPLANATIONS–