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Exercise Supplement

Module by: Wade Ellis, Denny Burzynski. E-mail the authorsEdited By: Math Editors

Summary: This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module is an exercise supplement for the chapter "Exponents, Roots, Factorization of Whole Numbers" and contains many exercise problems. Odd problems are accompanied by solutions.

Exercise Supplement

Exponents and Roots ((Reference))

For problems 1 -25, determine the value of each power and root.

Exercise 1

3333 size 12{3 rSup { size 8{3} } } {}

Solution

27

Exercise 2

4343 size 12{4 rSup { size 8{3} } } {}

Exercise 3

0505 size 12{0 rSup { size 8{5} } } {}

Solution

0

Exercise 4

1414 size 12{1 rSup { size 8{4} } } {}

Exercise 5

122122 size 12{"12" rSup { size 8{2} } } {}

Solution

144

Exercise 6

7272 size 12{7 rSup { size 8{2} } } {}

Exercise 7

8282 size 12{8 rSup { size 8{2} } } {}

Solution

64

Exercise 8

112112 size 12{"11" rSup { size 8{2} } } {}

Exercise 9

2525 size 12{2 rSup { size 8{5} } } {}

Solution

32

Exercise 10

3434 size 12{3 rSup { size 8{4} } } {}

Exercise 11

152152 size 12{"15" rSup { size 8{2} } } {}

Solution

225

Exercise 12

202202 size 12{"20" rSup { size 8{2} } } {}

Exercise 13

252252 size 12{"25" rSup { size 8{2} } } {}

Solution

625

Exercise 14

3636 size 12{ sqrt {"36"} } {}

Exercise 15

225225 size 12{ sqrt {"225"} } {}

Solution

15

Exercise 16

643643 size 12{ nroot { size 8{3} } {"64"} } {}

Exercise 17

164164 size 12{ nroot { size 8{4} } {"16"} } {}

Solution

2

Exercise 18

00 size 12{ sqrt {0} } {}

Exercise 19

1313 size 12{ nroot { size 8{3} } {1} } {}

Solution

1

Exercise 20

21632163 size 12{ nroot { size 8{3} } {"216"} } {}

Exercise 21

144144 size 12{ sqrt {"144"} } {}

Solution

12

Exercise 22

196196 size 12{ sqrt {"196"} } {}

Exercise 23

11 size 12{ sqrt {1} } {}

Solution

1

Exercise 24

0404 size 12{ nroot { size 8{4} } {0} } {}

Exercise 25

646646 size 12{ nroot { size 8{6} } {"64"} } {}

Solution

2

Section 3.2

For problems 26-45, use the order of operations to determine each value.

Exercise 26

23−2⋅423−2⋅4 size 12{2 rSup { size 8{3} } - 2 cdot 4} {}

Exercise 27

52−10⋅2−552−10⋅2−5 size 12{5 rSup { size 8{2} } - "10" cdot 2 - 5} {}

Solution

0

Exercise 28

81−32+6⋅281−32+6⋅2 size 12{ sqrt {"81"} - 3 rSup { size 8{2} } +6 cdot 2} {}

Exercise 29

152+52⋅22152+52⋅22 size 12{"15" rSup { size 8{2} } +5 rSup { size 8{2} } cdot 2 rSup { size 8{2} } } {}

Solution

325

Exercise 30

3⋅22+323⋅22+32 size 12{3 cdot left (2 rSup { size 8{2} } +3 rSup { size 8{2} } right )} {}

Exercise 31

64⋅32−2364⋅32−23 size 12{"64" cdot left (3 rSup { size 8{2} } - 2 rSup { size 8{3} } right )} {}

Solution

64

Exercise 32

52+113+33+11452+113+33+114 size 12{ { {5 rSup { size 8{2} } +1} over {"13"} } + { {3 rSup { size 8{3} } +1} over {"14"} } } {}

Exercise 33

62−15⋅7−49+72⋅762−15⋅7−49+72⋅7 size 12{ { {6 rSup { size 8{2} } - 1} over {5 cdot 7} } - { {"49"+7} over {2 cdot 7} } } {}

Solution

-3

Exercise 34

2⋅3+522+15⋅23−322⋅3+522+15⋅23−32 size 12{ { {2 cdot left [3+5 left (2 rSup { size 8{2} } +1 right ) right ]} over {5 cdot 2 rSup { size 8{3} } - 3 rSup { size 8{2} } } } } {}

Exercise 35

32⋅25−1423+252⋅52+5+232⋅25−1423+252⋅52+5+2 size 12{ { {3 rSup { size 8{2} } cdot left [2 rSup { size 8{5} } - 1 rSup { size 8{4} } left (2 rSup { size 8{3} } +"25" right ) right ]} over {2 cdot 5 rSup { size 8{2} } +5+2} } } {}

Solution

−957−957 size 12{ - { {9} over {"57"} } } {}

Exercise 36

52−23−2⋅722−1+5⋅32−32+152−23−2⋅722−1+5⋅32−32+1 size 12{ { { left (5 rSup { size 8{2} } - 2 rSup { size 8{3} } right ) - 2 cdot 7} over {2 rSup { size 8{2} } - 1} } +5 cdot left [ { {3 rSup { size 8{2} } - 3} over {2} } +1 right ]} {}

Exercise 37

8−32+2+3228−32+2+322 size 12{ left (8 - 3 right ) rSup { size 8{2} } + left (2+3 rSup { size 8{2} } right ) rSup { size 8{2} } } {}

Solution

146

Exercise 38

32⋅42+25+23⋅81−3232⋅42+25+23⋅81−32 size 12{3 rSup { size 8{2} } cdot left (4 rSup { size 8{2} } + sqrt {"25"} right )+2 rSup { size 8{3} } cdot left ( sqrt {"81"} - 3 rSup { size 8{2} } right )} {}

Exercise 39

16+916+9 size 12{ sqrt {"16"+9} } {}

Solution

5

Exercise 40

16+916+9 size 12{ sqrt {"16"} + sqrt {9} } {}

Exercise 41

Compare the results of problems 39 and 40. What might we conclude?

Solution

The sum of square roots is not necessarily equal to the square root of the sum.

Exercise 42

18⋅218⋅2 size 12{ sqrt {"18" cdot 2} } {}

Exercise 43

6⋅66⋅6 size 12{ sqrt {6 cdot 6} } {}

Solution

6

Exercise 44

7⋅77⋅7 size 12{ sqrt {7 cdot 7} } {}

Exercise 45

8⋅88⋅8 size 12{ sqrt {8 cdot 8} } {}

Solution

8

Exercise 46

An
records the number of identical factors that are repeated in a multiplication.

Prime Factorization of Natural Numbers ((Reference))

For problems 47- 53, find all the factors of each num­ber.

Exercise 47

18

Solution

1, 2, 3, 6, 9, 18

Exercise 48

24

Exercise 49

11

Solution

1, 11

Exercise 50

12

Exercise 51

51

Solution

1, 3, 17, 51,

Exercise 52

25

Exercise 53

2

Solution

1, 2

Exercise 54

What number is the smallest prime number?

Grouping Symbol and the Order of Operations ((Reference))

For problems 55 -64, write each number as a product of prime factors.

Exercise 55

55

Solution

5⋅115⋅11 size 12{5 cdot "11"} {}

Exercise 56

20

Exercise 57

80

Solution

24⋅524⋅5 size 12{2 rSup { size 8{4} } cdot 5} {}

Exercise 58

284

Exercise 59

700

Solution

22⋅52⋅722⋅52⋅7 size 12{2 rSup { size 8{2} } cdot 5 rSup { size 8{2} } cdot 7} {}

Exercise 60

845

Exercise 61

1,614

Solution

2⋅3⋅2692⋅3⋅269 size 12{2 cdot 3 cdot "269"} {}

Exercise 62

921

Exercise 63

29

Solution

29 is a prime number

Exercise 64

37

The Greatest Common Factor ((Reference))

For problems 65 - 75, find the greatest common factor of each collection of numbers.

Exercise 65

5 and 15

Solution

5

Exercise 66

6 and 14

Exercise 67

10 and 15

Solution

5

Exercise 68

6, 8, and 12

Exercise 69

18 and 24

Solution

6

Exercise 70

42 and 54

Exercise 71

40 and 60

Solution

20

Exercise 72

18, 48, and 72

Exercise 73

147, 189, and 315

Solution

21

Exercise 74

64, 72, and 108

Exercise 75

275, 297, and 539

Solution

11

The Least Common Multiple ((Reference))

For problems 76-86, find the least common multiple of each collection of numbers.

Exercise 76

5 and 15

Exercise 77

6 and 14

Solution

42

Exercise 78

10 and 15

Exercise 79

36 and 90

Solution

180

Exercise 80

42 and 54

Exercise 81

8, 12, and 20

Solution

120

Exercise 82

40, 50, and 180

Exercise 83

135, 147, and 324

Solution

79, 380

Exercise 84

108, 144, and 324

Exercise 85

5, 18, 25, and 30

Solution

450

Exercise 86

12, 15, 18, and 20

Exercise 87

Find all divisors of 24.

Solution

1, 2, 3, 4, 6, 8, 12, 24

Exercise 88

Find all factors of 24.

Exercise 89

Write all divisors of 23⋅52⋅723⋅52⋅7 size 12{2 rSup { size 8{3} } cdot 5 rSup { size 8{2} } cdot 7} {}.

Solution

1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 700, 1,400

Exercise 90

Write all divisors of 6⋅82⋅1036⋅82⋅103 size 12{6 cdot 8 rSup { size 8{2} } cdot "10" rSup { size 8{3} } } {}.

Exercise 91

Does 7 divide 53⋅64⋅72⋅8553⋅64⋅72⋅85 size 12{5 rSup { size 8{3} } cdot 6 rSup { size 8{4} } cdot 7 rSup { size 8{2} } cdot 8 rSup { size 8{5} } } {}?

Solution

yes

Exercise 92

Does 13 divide 83⋅102⋅114⋅132⋅1583⋅102⋅114⋅132⋅15 size 12{8 rSup { size 8{3} } cdot "10" rSup { size 8{2} } cdot "11" rSup { size 8{4} } cdot "13" rSup { size 8{2} } cdot "15"} {}?

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