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

where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
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?
what is a peer
What is meant by 'nano scale'?
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
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
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?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
From 1973 to 1979, in the United States, there was an increase of 166.6% of Ph.D. social scien­tists to 52,000. How many were there in 1973?
7hours 36 min - 4hours 50 min