Download Exponents, Roots and Radicals

1) For how many positive integers is 100
 x2  200 ? (1) 2004-WU2-3
2) When the expression 810  522 is multiplied out. How many digits does the
number have? (2) 2004-WU6-6
3) When simplified, what is the value of (100.5)(100.3)(100.2)(100.1)(100.9) ? (2)
2004-WU9-10
4) What is the value of
æ 2 1ö
5) Evaluate ç + ÷
è 3 2ø
20 + 20 + 20 + 20 + ... ? (3) 2004-WU14-5
-3
. Express your answer as a common fraction. (2) 1999-
WU3-4
6) Find the integer n such that n  34  75 = 216 (2) 1999-WU5-7
7) Evaluate:
3
( 7!) ( 7!) ( 8!) . (3) 1999-WU6-3
8) What is the sum of all values of x for which
( x + 3)2
= 7 ? (2) 1999-
WU7-2
9) Evaluate:
10) Evaluate:
(6!)(4!)(2!)(0!)
. (2) 1999-WU11-5
5i3
3
27 2 - 4 16 2 . (2) 1999-WU12-2
11) How many digits are in the number 2521  248 ? (2) 1999-WU14-6
12) What is the value of n such that
10 n = 10-5 ´
10 73
0.001
? (3) 2000-WU11-2
13) The formula used to estimate the speed of a vehicle at an accident is
s = 5 l , where s represents the speed in miles per hour and l represents
the length of the tire skid mark in feet. What is the speed when the length
of the skid mark measures 245 feet? Round to the nearest tenth. (1) 2000WU11-7
14) In computer jargon, 1 nibble = ½ byte, 1024 bytes = 1 kilobyte, and 1024
kilobytes = 1 megabyte. Expressed as a power of 2, how many nibbles are in
1 megabyte? (1) 2000-WU11-8
15) Suppose
p
2p
= 3 . What is the value of
? Express your answer in
q
p-q
simplest radical form. (3) 2000-WU12-3
16) What is the value of n such that 2n = 44  88  1616 ? (2) 2000-WU12-8

17) What is the value of (57 + 57 + 57 + 57 + 57) ? (3) 2000-WU15-7
18) What integer is closest to the value of
5
1000 ?
19) What is the least possible integer-value of n such that
integer? 2003-WU8-8 (2)
20) If
21) If
18 × n × 34 is an
(2 3 )(2 ) = 2 n , what is the value of n? 2003-W11-6 (2)
3
4x + 4x + 4x + ... = 10 , what is the value of x? Round to the nearest
tenth. (3) 2003-WO6-4
22) Solve for the positive value of m:
23) Solve for x:
8 x-1 = 4 x+1 .
2
3
m = 4.
(3) 1997-WU10-8
(2) 1997-WU8-8
24) Given that 63 + 63 + 63 + 63 + 63 + 63 = 6x and 22 + 22 = 2y, what is the value of
xy? (3) 1997-WU11-4
100
2.5
=
. (3) 1997-WU12-8
4
x
25) Solve for x:
26) How many combinations of
yield integer values for
x
2 £ x £ 9 and 2 £ y £ 100 for integers x and y will
y ? (2) 1997-WU15-10
27) Solve for x: 8x = 32. (3) 1997-WO3-10
28) If n is an integer and 20 < 2n < 200, what is the sum of all of the possible
values of n? (2) 2001-WO9-10
29) Find x:
20
20
=
(2) 1996-WU3-7
50
x
30) How many natural numbers are between
10 and
90 ? (1) 1996-WU9-10
312 - 310
31) Compute: 10
(3) 1996-WU10-6
3 - 38
32) Evaluate: 27
-
1
3
+ 32
-
2
5
(3) 1996-WU14-3
33) Solve for x: 4(24) + 2(42) + 2(23) + 24 = 2x (3) 1996-WO9-10
34) 37  36 =
n × 36 .
Find n. (3) 1993-WU2-3
35) Express (51 + 41)1 as a common fraction. (2) 1993-WU3-2
36) Express in simplest form: (2)4x + 2(2)6x  5(8)x. (3) 1993-WU15-8
37) If 85 + 85 + 85 + 85 + 85 + 85 + 85 + 85 = 2x, what is the value of x? (3) 1993WU15-10
38) If 6x = 24, what is the value of 62x  1 ? (3) 1993-WU17-6
39) If 2x = 7, find the value of 23x + 2 . (3) 1993-WU19-9
40) If 2a = 32 and ab = 625, find a + b. (2) 1993-WO5-9
-
41) Evaluate: (16)
42) Find x:
1
4
-
2
3
- (8) . (3) 1995-WU5-3
x = 2 . (1) 1995-WU16-3
43) Find a three-digit number such that the cube of the sum of its digits is equal
to the number. (1) 1995-WO4-10
44) What is the largest integral value of x for which
WO6-2
x + x < 10 ? (1) 1995-
Exponents, Roots and Radicals – Answer Key
148077365
1) 5
2) 25
3) 100
4) 5
5) 216/343
6) 63
7) 10,800
8) 6
9) 18
10) 5
11) 44
12) 33
13) 78 mph
14) 221
15)
3+ 3
16) 96
17) 25
18) 4
19) 17
20) 24
21) 22.5
22) 8
23) 5
6
148077365
24) 64
25) 1/10
26) 16
27) 5/3
28) 18
29) 125
30) 6
31) 9
32) 7/12
33) 7
34) 2
35) 20/9
36) 213x3
37) 18
38) 96
39) 1372
40) 9
41) ¼
42) 65,536
43) 512
44) 7
7
148077365
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