3.7: Exercise Supplement

Fundamentals of Mathematics · LibreTexts

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    Exponents and Roots

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

    Exercise \(\PageIndex{1}\)

    \(3^3\)

    Answer

    27

    Exercise \(\PageIndex{2}\)

    \(4^3\)

    Exercise \(\PageIndex{3}\)

    \(0^5\)

    Answer

    0

    Exercise \(\PageIndex{4}\)

    \(1^4\)

    Exercise \(\PageIndex{5}\)

    \(12^2\)

    Answer

    144

    Exercise \(\PageIndex{6}\)

    \(7^2\)

    Exercise \(\PageIndex{7}\)

    \(8^2\)

    Answer

    64

    Exercise \(\PageIndex{8}\)

    \(11^2\)

    Exercise \(\PageIndex{9}\)

    \(2^5\)

    Answer

    32

    Exercise \(\PageIndex{10}\)

    \(3^4\)

    Exercise \(\PageIndex{11}\)

    \(15^2\)

    Answer

    225

    Exercise \(\PageIndex{12}\)

    \(20^2\)

    Exercise \(\PageIndex{13}\)

    \(25^2\)

    Answer

    625

    Exercise \(\PageIndex{14}\)

    \(\sqrt{36}\)

    Exercise \(\PageIndex{15}\)

    \(\sqrt{225}\)

    Answer

    15

    Exercise \(\PageIndex{16}\)

    \(\sqrt[3]{64}\)

    Exercise \(\PageIndex{17}\)

    \(\sqrt[4]{16}\)

    Answer

    2

    Exercise \(\PageIndex{18}\)

    \(\sqrt{0}\)

    Exercise \(\PageIndex{19}\)

    \(\sqrt[3]{1}\)

    Answer

    1

    Exercise \(\PageIndex{20}\)

    \(\sqrt[3]{216}\)

    Exercise \(\PageIndex{21}\)

    \(\sqrt{144}\)

    Answer

    12

    Exercise \(\PageIndex{22}\)

    \(\sqrt{196}\)

    Exercise \(\PageIndex{23}\)

    \(\sqrt{1}\)

    Answer

    1

    Exercise \(\PageIndex{24}\)

    \(\sqrt[4]{0}\)

    Exercise \(\PageIndex{25}\)

    \(\sqrt[6]{64}\)

    Answer

    2

    Section 3.2

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

    Exercise \(\PageIndex{26}\)

    \(2^3 - 2 \cdot 4\)

    Exercise \(\PageIndex{27}\)

    \(5^2 - 10 \cdot 2 - 5\)

    Answer

    0

    Exercise \(\PageIndex{28}\)

    \(\sqrt{81} - 3^2 + 6 \cdot 2\)

    Exercise \(\PageIndex{29}\)

    \(15^2 + 5^2 \cdot 2^2\)

    Answer

    325

    Exercise \(\PageIndex{30}\)

    \(3 \cdot (2^2 + 3^2)\)

    Exercise \(\PageIndex{31}\)

    \(64 \cdot (3^2 - 2^3)\)

    Answer

    64

    Exercise \(\PageIndex{32}\)

    \(\dfrac{5^2 + 1}{13} + \dfrac{3^3 + 1}{14}\)

    Exercise \(\PageIndex{33}\)

    \(\dfrac{6^2 - 1}{5 \cdot 7} - \dfrac{49 + 7}{2 \cdot 7}\)

    Answer

    -3

    Exercise \(\PageIndex{34}\)

    \(\dfrac{2 \cdot [3 + 5(2^2 + 1)]}{5 \cdot 2^3 - 3^2}\)

    Exercise \(\PageIndex{35}\)

    \(\dfrac{3^2 \cdot [2^5 - 1^4 (2^3 + 25)]}{2 \cdot 5^2 + 5 + 2}\)

    Answer

    \(-\dfrac{9}{57}\)

    Exercise \(\PageIndex{36}\)

    \(\dfrac{(5^2 - 2^3) - 2 \cdot 7}{2^2 - 1} + 5 \cdot [\dfrac{3^2 - 3}{2} + 1]\)

    Exercise \(\PageIndex{37}\)

    \((8 - 3)^2 + (2 + 3^2)^2\)

    Answer

    146

    Exercise \(\PageIndex{38}\)

    \(3^2 \cdot (4^2 + \sqrt{25}) + 2^3 \cdot (\sqrt{81} - 3^2)\)

    Exercise \(\PageIndex{39}\)

    \(\sqrt{16 + 9}}\)

    Answer

    5

    Exercise \(\PageIndex{40}\)

    \(\sqrt{16} + \sqrt{9}\)

    Exercise \(\PageIndex{41}\)

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

    Answer

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

    Exercise \(\PageIndex{42}\)

    \(\sqrt{18 \cdot 2}\)

    Exercise \(\PageIndex{43}\)

    \(\sqrt{6 \cdot 6}\)

    Answer

    6

    Exercise \(\PageIndex{44}\)

    \(\sqrt{7 \cdot 7}\)

    Exercise \(\PageIndex{45}\)

    \(\sqrt{8 \cdot 8}\)

    Answer

    8

    Exercise \(\PageIndex{46}\)

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

    Prime Factorization of Natural Numbers

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

    Exercise \(\PageIndex{47}\)

    18

    Answer

    1, 2, 3, 6, 9, 18

    Exercise \(\PageIndex{48}\)

    24

    Exercise \(\PageIndex{49}\)

    11

    Answer

    1, 11

    Exercise \(\PageIndex{50}\)

    12

    Exercise \(\PageIndex{51}\)

    51

    Answer

    1, 3, 17, 51,

    Exercise \(\PageIndex{52}\)

    25

    Exercise \(\PageIndex{53}\)

    2

    Answer

    1, 2

    Exercise \(\PageIndex{54}\)

    What number is the smallest prime number?

    Grouping Symbol and the Order of Operations

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

    Exercise \(\PageIndex{55}\)

    55

    Answer

    \(5 \cdot 11\)

    Exercise \(\PageIndex{56}\)

    20

    Exercise \(\PageIndex{57}\)

    80

    Answer

    \(2^4 \cdot 5\)

    Exercise \(\PageIndex{58}\)

    284

    Exercise \(\PageIndex{59}\)

    700

    Answer

    \(2^2 \cdot 5^2 \cdot 7\)

    Exercise \(\PageIndex{60}\)

    845

    Exercise \(\PageIndex{61}\)

    1,614

    Answer

    \(2 \cdot 3 \cdot 269\)

    Exercise \(\PageIndex{62}\)

    921

    Exercise \(\PageIndex{63}\)

    29

    Answer

    29 is a prime number

    Exercise \(\PageIndex{64}\)

    37

    The Greatest Common Factor

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

    Exercise \(\PageIndex{65}\)

    5 and 15

    Answer

    5

    Exercise \(\PageIndex{66}\)

    6 and 14

    Exercise \(\PageIndex{67}\)

    10 and 15

    Answer

    5

    Exercise \(\PageIndex{68}\)

    6, 8, and 12

    Exercise \(\PageIndex{69}\)

    18 and 24

    Answer

    6

    Exercise \(\PageIndex{70}\)

    42 and 54

    Exercise \(\PageIndex{71}\)

    40 and 60

    Answer

    20

    Exercise \(\PageIndex{72}\)

    18, 48, and 72

    Exercise \(\PageIndex{73}\)

    147, 189, and 315

    Answer

    21

    Exercise \(\PageIndex{74}\)

    64, 72, and 108

    Exercise \(\PageIndex{75}\)

    275, 297, and 539

    Answer

    11

    The Least Common Multiple

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

    Exercise \(\PageIndex{76}\)

    5 and 15

    Exercise \(\PageIndex{77}\)

    6 and 14

    Answer

    42

    Exercise \(\PageIndex{78}\)

    10 and 15

    Exercise \(\PageIndex{79}\)

    36 and 90

    Answer

    180

    Exercise \(\PageIndex{80}\)

    42 and 54

    Exercise \(\PageIndex{81}\)

    8, 12, and 20

    Answer

    120

    Exercise \(\PageIndex{82}\)

    40, 50, and 180

    Exercise \(\PageIndex{83}\)

    135, 147, and 324

    Answer

    79, 380

    Exercise \(\PageIndex{84}\)

    108, 144, and 324

    Exercise \(\PageIndex{85}\)

    5, 18, 25, and 30

    Answer

    450

    Exercise \(\PageIndex{86}\)

    12, 15, 18, and 20

    Exercise \(\PageIndex{87}\)

    Find all divisors of 24.

    Answer

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

    Exercise \(\PageIndex{88}\)

    Find all factors of 24.

    Exercise \(\PageIndex{89}\)

    Write all divisors of \(2^3 \cdot 5^2 \cdot 7\).

    Answer

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

    Exercise \(\PageIndex{90}\)

    Write all divisors of \(6 \cdot 8^2 \cdot 10^3\).

    Exercise \(\PageIndex{91}\)

    Does 7 divide \(5^3 \cdot 6^4 \cdot 7^2 \cdot 8^5\)?

    Answer

    yes

    Exercise \(\PageIndex{86}\)

    Does 13 divide \(8^3 \cdot 10^2 \cdot 11^4 \cdot 13^2 \cdot 15\)?

    This page titled 3.7: Exercise Supplement was last modified on Sat, 08 Jun 2024 18:05:10 GMT and is shared under a CC BY license and was authored, remixed, and/or curated by Denny Burzynski and Wade Ellis, Jr. (OpenStax CNX) via source content that was edited to the style and standards of the LibreTexts platform.