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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.

Exercise supplement

Exponents and roots ( [link] )

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

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

27

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

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

0

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

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

144

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

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

64

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

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

32

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

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

225

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

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

625

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

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

15

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

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

2

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0 size 12{ sqrt {0} } {}

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

1

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

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

12

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

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1 size 12{ sqrt {1} } {}

1

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

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

2

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Section 3.2

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

2 3 2 4 size 12{2 rSup { size 8{3} } - 2 cdot 4} {}

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5 2 10 2 5 size 12{5 rSup { size 8{2} } - "10" cdot 2 - 5} {}

0

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81 3 2 + 6 2 size 12{ sqrt {"81"} - 3 rSup { size 8{2} } +6 cdot 2} {}

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15 2 + 5 2 2 2 size 12{"15" rSup { size 8{2} } +5 rSup { size 8{2} } cdot 2 rSup { size 8{2} } } {}

325

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3 2 2 + 3 2 size 12{3 cdot left (2 rSup { size 8{2} } +3 rSup { size 8{2} } right )} {}

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64 3 2 2 3 size 12{"64" cdot left (3 rSup { size 8{2} } - 2 rSup { size 8{3} } right )} {}

64

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5 2 + 1 13 + 3 3 + 1 14 size 12{ { {5 rSup { size 8{2} } +1} over {"13"} } + { {3 rSup { size 8{3} } +1} over {"14"} } } {}

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6 2 1 5 7 49 + 7 2 7 size 12{ { {6 rSup { size 8{2} } - 1} over {5 cdot 7} } - { {"49"+7} over {2 cdot 7} } } {}

-3

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2 3 + 5 2 2 + 1 5 2 3 3 2 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} } } } } {}

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3 2 2 5 1 4 2 3 + 25 2 5 2 + 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} } } {}

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

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5 2 2 3 2 7 2 2 1 + 5 3 2 3 2 + 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 ]} {}

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8 3 2 + 2 + 3 2 2 size 12{ left (8 - 3 right ) rSup { size 8{2} } + left (2+3 rSup { size 8{2} } right ) rSup { size 8{2} } } {}

146

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3 2 4 2 + 25 + 2 3 81 3 2 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 )} {}

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

5

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

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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.

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

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6 6 size 12{ sqrt {6 cdot 6} } {}

6

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7 7 size 12{ sqrt {7 cdot 7} } {}

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8 8 size 12{ sqrt {8 cdot 8} } {}

8

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

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Prime factorization of natural numbers ( [link] )

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

What number is the smallest prime number?

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

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

55

5 11 size 12{5 cdot "11"} {}

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80

2 4 5 size 12{2 rSup { size 8{4} } cdot 5} {}

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700

2 2 5 2 7 size 12{2 rSup { size 8{2} } cdot 5 rSup { size 8{2} } cdot 7} {}

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1,614

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

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The greatest common factor ( [link] )

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

The least common multiple ( [link] )

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

135, 147, and 324

79, 380

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Find all divisors of 24.

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

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Write all divisors of 2 3 5 2 7 size 12{2 rSup { size 8{3} } cdot 5 rSup { size 8{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

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

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Does 7 divide 5 3 6 4 7 2 8 5 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} } } {} ?

yes

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Does 13 divide 8 3 10 2 11 4 13 2 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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Questions & Answers

what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
how to synthesize TiO2 nanoparticles by chemical methods
Zubear
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
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