57. d.Apply the order of operations and exponent
    rules:

–(^25 )^0 (–3^2 + 2– 3)–1= –1( – 9 + )–1

= –1( – 9 + ^18 )–1

= –1(–^782 + ^18 )–1

= –1(–^781 )–1

= –1(– 781 )

=  781 

58. c.Apply the order of operations and exponent
    rules:
    4 – 2(1 – 2(–1)– 3)– 2=  412 1 – 2–^11 

3



• 
  

  2

  
  

 116 (1 – 2( – 1))– 2=  116 (3)– 2=  116  31  (^2) =
 1144 =  112  2 = 12–2

59. d.Apply the order of operations and exponent
    rules:

–2– 2+ = – + =

• ^14 + = –^14 + = –^14 + =


• ^14 –  116 = – 156 

60. c.Simplify each expression:

(–^14 )–1= (–4)^1 = –4

–= ––^32 = ^32 

4(–^14 ) + 3 = –1 + 3 = 2

–(–^14 )^0 = –(1) = –1

Hence, the expression with the largest value is

4(–^14 ) + 3.

61. d.The reciprocal of a fraction pstrictly
    between 0 and 1 is necessarily larger than 1.
    So,p–11. Also, raising a fraction pstrictly
    between 0 and 1to a positive integer power
    results in a fraction with a smaller value. (To
    see this, try it out with p = ^12 .) As such, both p^2
    and p^3 are less than pand are not larger than
    
    
    1. So, of the four expressions provided, the one
       with the largest value isp–^1.
    
    
    
    


62. c.The reciprocal of a fraction pstrictly
    between 0 and 1 is necessarily larger than 1.
    So,p– 11. Raising a fraction pstrictly
    between 0 and 1 to a positive integer power
    results in a fraction with a smaller value. (Try
    this out withp = ^12 .) We know that 0p^3 
    p^2 p1. Therefore, of the four expressions
    provided, the one with the smallest value is p^3.


63. b.Note that the expressions p,p^3 , and p–1are
    all negative since it is assumed that pis a frac-
    tion between –1 and 0. Since squaring a nega-
    tive fraction results in a positive 1, we conclude
    that p^2 is positive and is, therefore, the largest
    of the four choices.


64. c.Raising a fraction strictly between 1 and 2 to
    a positive integer power results in a larger frac-
    tion. Thus, we know that 1pp^2 .Moreover,
    the reciprocals of fractions larger than 1 are
    necessarily less than 1. In particular,p–11,
    which shows thatp–1is smaller than both p
    and p^2. Finally, multiplying both sides of the
    inequality ,p–1 1 by p–1shows that p–2= p–1
    p–1p–1. Therefore, we conclude that the
    smallest of the four expressions is p–2.

Set 5 (Page 8)

65. a.The quantity n% means “nparts out of
    100.” It can be written as  1 n 00 or equivalently as
    n0.01. Applying this to 40 yields the equiva-
    lent expressions I and II.


66. d.The result of increasing 48 by 55% is given
    by 48 + 0.55(48) = 74.4.


67. d.The price resulting from discounting $250
    by 25% is given by $250 – 0.25($250). This
    quantity is equivalent to both 0.75$250 and
    (1 – 0.25)$250.

^3

8(–^14 )

^14 

–4

(–^1 2) 2

(–2) –4

–2

–4

(– 1 + (–1))–2

–4

^1

22

(–1^3 +(–1)^3 )– 2

–2^2

^1

23

ANSWERS & EXPLANATIONS–