# 3.7 Exercise supplement

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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.

## Exponents and roots ( [link] )

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

${3}^{3}$

27

${4}^{3}$

${0}^{5}$

0

${1}^{4}$

${\text{12}}^{2}$

144

${7}^{2}$

${8}^{2}$

64

${\text{11}}^{2}$

${2}^{5}$

32

${3}^{4}$

${\text{15}}^{2}$

225

${\text{20}}^{2}$

${\text{25}}^{2}$

625

$\sqrt{\text{36}}$

$\sqrt{\text{225}}$

15

$\sqrt[3]{\text{64}}$

$\sqrt[4]{\text{16}}$

2

$\sqrt{0}$

$\sqrt[3]{1}$

1

$\sqrt[3]{\text{216}}$

$\sqrt{\text{144}}$

12

$\sqrt{\text{196}}$

$\sqrt{1}$

1

$\sqrt[4]{0}$

$\sqrt[6]{\text{64}}$

2

## Section 3.2

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

${2}^{3}-2\cdot 4$

${5}^{2}-\text{10}\cdot 2-5$

0

$\sqrt{\text{81}}-{3}^{2}+6\cdot 2$

${\text{15}}^{2}+{5}^{2}\cdot {2}^{2}$

325

$3\cdot \left({2}^{2}+{3}^{2}\right)$

$\text{64}\cdot \left({3}^{2}-{2}^{3}\right)$

64

$\frac{{5}^{2}+1}{\text{13}}+\frac{{3}^{3}+1}{\text{14}}$

$\frac{{6}^{2}-1}{5\cdot 7}-\frac{\text{49}+7}{2\cdot 7}$

-3

$\frac{2\cdot \left[3+5\left({2}^{2}+1\right)\right]}{5\cdot {2}^{3}-{3}^{2}}$

$\frac{{3}^{2}\cdot \left[{2}^{5}-{1}^{4}\left({2}^{3}+\text{25}\right)\right]}{2\cdot {5}^{2}+5+2}$

$-\frac{9}{\text{57}}$

$\frac{\left({5}^{2}-{2}^{3}\right)-2\cdot 7}{{2}^{2}-1}+5\cdot \left[\frac{{3}^{2}-3}{2}+1\right]$

${\left(8-3\right)}^{2}+{\left(2+{3}^{2}\right)}^{2}$

146

${3}^{2}\cdot \left({4}^{2}+\sqrt{\text{25}}\right)+{2}^{3}\cdot \left(\sqrt{\text{81}}-{3}^{2}\right)$

$\sqrt{\text{16}+9}$

5

$\sqrt{\text{16}}+\sqrt{9}$

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

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

$\sqrt{\text{18}\cdot 2}$

$\sqrt{6\cdot 6}$

6

$\sqrt{7\cdot 7}$

$\sqrt{8\cdot 8}$

8

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

## Prime factorization of natural numbers ( [link] )

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

18

1, 2, 3, 6, 9, 18

24

11

1, 11

12

51

1, 3, 17, 51,

25

2

1, 2

What number is the smallest prime number?

## Grouping symbol and the order of operations ( [link] )

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

55

$5\cdot \text{11}$

20

80

${2}^{4}\cdot 5$

284

700

${2}^{2}\cdot {5}^{2}\cdot 7$

845

1,614

$2\cdot 3\cdot \text{269}$

921

29

29 is a prime number

37

## The greatest common factor ( [link] )

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

5 and 15

5

6 and 14

10 and 15

5

6, 8, and 12

18 and 24

6

42 and 54

40 and 60

20

18, 48, and 72

147, 189, and 315

21

64, 72, and 108

275, 297, and 539

11

## The least common multiple ( [link] )

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

5 and 15

6 and 14

42

10 and 15

36 and 90

180

42 and 54

8, 12, and 20

120

40, 50, and 180

135, 147, and 324

79, 380

108, 144, and 324

5, 18, 25, and 30

450

12, 15, 18, and 20

Find all divisors of 24.

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

Find all factors of 24.

Write all divisors of ${2}^{3}\cdot {5}^{2}\cdot 7$ .

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

Write all divisors of $6\cdot {8}^{2}\cdot {\text{10}}^{3}$ .

Does 7 divide ${5}^{3}\cdot {6}^{4}\cdot {7}^{2}\cdot {8}^{5}$ ?

yes

Does 13 divide ${8}^{3}\cdot {\text{10}}^{2}\cdot {\text{11}}^{4}\cdot {\text{13}}^{2}\cdot \text{15}$ ?

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absolutely yes
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for teaching engĺish at school how nano technology help us
Anassong
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s.
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in general
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