OpenStax-CNX module: m34879
1
Exponents, Roots, Factorization of
∗
Whole Numbers: Proficiency Exam
Wade Ellis
Denny Burzynski
This work is produced by OpenStax-CNX and licensed under the
Creative Commons Attribution License 3.0†
Abstract
This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This
module is a prociency exam to the chapter "Exponents, Roots, Factorization of Whole Numbers." Each
problem is accompanied with a reference link pointing back to the module that discusses the type of
problem demonstrated in the question. The problems in this exam are accompanied by solutions.
1 Prociency Exam
Exercise 1
(Solution on p. 3.)
Exercise 2
(Solution on p. 3.)
Exercise 3
(Solution on p. 3.)
Exercise 4
(Solution on p. 3.)
Exercise 5
(Solution on p. 3.)
Exercise 6
(Solution on p. 3.)
Exercise 7
(Solution on p. 3.)
Exercise
8
√
(Solution on p. 3.)
Exercise
9
√
(Solution on p. 3.)
() In the number 85 , write the names used for the number 8 and the number 5.
() Write using exponents. 12 × 12 × 12 × 12 × 12 × 12 × 12
() Expand 94 .
For problems 4-15, determine the value of each expression.
() 43
() 15
() 03
() 26
49
()
()
3
∗ Version
27
1.2: Aug 18, 2010 8:25 pm -0500
† http://creativecommons.org/licenses/by/3.0/
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OpenStax-CNX module: m34879
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Exercise
10
√
(Solution on p. 3.)
Exercise 11
(Solution on p. 3.)
Exercise
√ 12
(Solution on p. 3.)
()
8
1
() 16 + 2 · (8 − 6)
() 53 − 100 + 8 · 2 − 20 ÷ 5
Exercise 13
() 3 ·
82 −2·32
52 −2
(Solution on p. 3.)
·
63 −4·52
29
Exercise 14
()
20+2
4
23 ·2−5·2
·
(Solution on p. 3.)
√
5·7− 81
7+3·2
Exercise
15
h
√ i
() (8 − 3)2 + 33 − 4 49
(Solution on p. 3.)
−2
10 − 32 + 9 − 5
For problems 16-20, nd the prime factorization of each whole number. If the number is prime, write "prime."
Exercise 16
(Solution on p. 3.)
Exercise 17
(Solution on p. 3.)
Exercise 18
(Solution on p. 3.)
Exercise 19
(Solution on p. 3.)
Exercise 20
(Solution on p. 3.)
Exercise 21
(Solution on p. 3.)
Exercise 22
(Solution on p. 3.)
Exercise 23
(Solution on p. 3.)
Exercise 24
(Solution on p. 3.)
Exercise 25
(Solution on p. 3.)
Exercise 26
(Solution on p. 4.)
Exercise 27
(Solution on p. 4.)
Exercise 28
(Solution on p. 4.)
Exercise 29
(Solution on p. 4.)
() 18
() 68
() 142
() 151
() 468
For problems 21 and 22, nd the greatest common factor.
() 200 and 36
() 900 and 135
() Write all the factors of 36.
() Write all the divisors of 18.
() Does 7 divide into 52 · 63 · 74 · 8? Explain.
() Is 3 a factor of 26 · 32 · 53 · 46 ? Explain.
() Does 13 divide into 113 · 124 · 152 ? Explain.
For problems 28 and 29, nd the least common multiple.
() 432 and 180
() 28, 40, and 95
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OpenStax-CNX module: m34879
Solutions to Exercises in this Module
Solution to Exercise (p. 1)
base; exponent
Solution to Exercise (p. 1)
127
Solution to Exercise (p. 1)
94 = 9 · 9 · 9 · 9 = 6, 561
Solution to Exercise (p. 1)
64
Solution to Exercise (p. 1)
1
Solution to Exercise (p. 1)
0
Solution to Exercise (p. 1)
64
Solution to Exercise (p. 1)
7
Solution to Exercise (p. 1)
3
Solution to Exercise (p. 2)
1
Solution to Exercise (p. 2)
20
Solution to Exercise (p. 2)
127
Solution to Exercise (p. 2)
24
Solution to Exercise (p. 2)
8
Solution to Exercise (p. 2)
5
Solution to Exercise (p. 2)
32 · 2
Solution to Exercise (p. 2)
22 · 17
Solution to Exercise (p. 2)
2 · 71
Solution to Exercise (p. 2)
prime
Solution to Exercise (p. 2)
22 · 32 · 13
Solution to Exercise (p. 2)
4
Solution to Exercise (p. 2)
45
Solution to Exercise (p. 2)
1, 2, 3, 4, 6, 9, 12, 18, 36
Solution to Exercise (p. 2)
1, 2, 3, 6, 9, 18
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OpenStax-CNX module: m34879
Solution to Exercise (p. 2)
Yes, because one of the (prime) factors of the number is 7.
Solution to Exercise (p. 2)
Yes, because it is one of the factors of the number.
Solution to Exercise (p. 2)
No, because the prime 13 is not a factor any of the listed factors of the number.
Solution to Exercise (p. 2)
2,160
Solution to Exercise (p. 2)
5,320
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