Roots, Radicals and Exponents
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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 20 + 20 + 20 + 20 + ... ? (3) 2004-WU14-5
-3 æ 2 1ö 5) Evaluate ç + ÷ . Express your answer as a common fraction. (2) è 3 2ø
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
2 8) What is the sum of all values of x for which ( x + 3) = 7 ? (2) 1999- WU7-2
(6!)(4!)(2!)(0!) 9) Evaluate: . (2) 1999-WU11-5 5i3
10) Evaluate: 3 272 - 4 162 . (2) 1999-WU12-2
11) How many digits are in the number 2521 248 ? (2) 1999-WU14-6 n -5 1073 12) What is the value of n such that 10 = 10 ´ 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) 2000- WU11-7
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
p 2 p = 3 15) Suppose q . What is the value of p - q ? Express your answer in 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 18 × n × 34 is an integer? 2003-WU8-8 (2)
3 20) If (23 )(2 ) = 2n , what is the value of n? 2003-W11-6 (2)
21) If 4x + 4x + 4x + ... = 10, what is the value of x? Round to the nearest tenth. (3) 2003-WO6-4
2 22) Solve for the positive value of m: m 3 = 4 . (2) 1997-WU8-8
23) Solve for x: 8x-1 = 4 x+1 . (3) 1997-WU10-8 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 25) Solve for x: = . (3) 1997-WU12-8 4 x
26) How many combinations of 2 £ x £ 9 and 2 £ y £ 100 for integers x and y will yield integer values for x 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
20 20 29) Find x: = (2) 1996-WU3-7 50 x
30) How many natural numbers are between 10 and 90 ? (1) 1996-WU9-10
312 - 310 31) Compute: (3) 1996-WU10-6 310 - 38
1 2 - - 32) Evaluate: 27 3 + 32 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 (51 + 41)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) 1993- WU15-10 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
1 2 - - 41) Evaluate: (16) 4 - (8) 3 . (3) 1995-WU5-3
42) Find x: 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 x + x < 10? (1) 1995- WO6-2 Exponents, Roots and Radicals – Answer Key 03ad5ab58b536982f33abcf109963d63.doc 6
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 03ad5ab58b536982f33abcf109963d63.doc 7
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) 213x3
37) 18
38) 96
39) 1372
40) 9
41) ¼
42) 65,536
43) 512
44) 7 03ad5ab58b536982f33abcf109963d63.doc 8