<< Chapter < Page Chapter >> Page >
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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

0

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

144

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

64

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

32

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

225

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

625

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

15

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

2

Got questions? Get instant answers now!

0 size 12{ sqrt {0} } {}

Got questions? Get instant answers now!

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

1

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

12

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

1 size 12{ sqrt {1} } {}

1

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

2

Got questions? Get instant answers now!

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} {}

Got questions? Get instant answers now!

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

0

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

64

Got questions? Get instant answers now!

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"} } } {}

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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} } } } } {}

Got questions? Get instant answers now!

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"} } } {}

Got questions? Get instant answers now!

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 ]} {}

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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 )} {}

Got questions? Get instant answers now!

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

5

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

6

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

8

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

Prime factorization of natural numbers ( [link] )

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

What number is the smallest prime number?

Got questions? Get instant answers now!

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"} {}

Got questions? Get instant answers now!

80

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

Got questions? Get instant answers now!

700

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

Got questions? Get instant answers now!

1,614

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

Find all divisors of 24.

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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"} {} ?

Got questions? Get instant answers now!

Questions & Answers

I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
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
How can I make nanorobot?
Lily
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
7hours 36 min - 4hours 50 min
Tanis Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Fundamentals of mathematics' conversation and receive update notifications?

Ask