# 3.9 Exercise supplement

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This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr. The basic operations with real numbers are presented in this chapter. The concept of absolute value is discussed both geometrically and symbolically. The geometric presentation offers a visual understanding of the meaning of |x|. The symbolic presentation includes a literal explanation of how to use the definition. Negative exponents are developed, using reciprocals and the rules of exponents the student has already learned. Scientific notation is also included, using unique and real-life examples.This module contains the exercise supplement for the chapter "Basic Operations with Real Numbers".

## Signed numbers ( [link] )

For the following problems, find $-a$ if $a$ is

27

$-27$

$-15$

$-\frac{8}{9}$

$\frac{8}{9}$

$-\left(-3\right)$

$k$

$-k$

## Absolute value ( [link] )

Simplify the following problems.

$|8|$

$|-3|$

3

$-|16|$

$-\left(-|12|\right)$

12

$-|0|$

## Addition of signed numbers ( [link] ) - multiplication and division of signed numbers ( [link] )

Simplify the following problems.

$4+\left(-6\right)$

$-2$

$-16+\left(-18\right)$

$3-\left(-14\right)$

17

$\left(-5\right)\left(2\right)$

$\left(-6\right)\left(-3\right)$

18

$\left(-1\right)\left(-4\right)$

$\left(4\right)\left(-3\right)$

$-12$

$\frac{-25}{5}$

$\frac{-100}{-10}$

10

$16-18+5$

$\frac{\left(-2\right)\left(-4\right)+10}{-5}$

$-\frac{18}{5}$

$\frac{-3\left(-8+4\right)-12}{4\left(3+6\right)-2\left(-8\right)}$

$\frac{-1\left(-3-2\right)-4\left(-4\right)}{-13+10}$

$-7$

$-\left(2-10\right)$

$0-6\left(-4\right)\left(-2\right)$

$-48$

## Multiplication and division of signed numbers ( [link] )

Find the value of each expression for the following problems.

$P=R-C$ . Find $P$ if $R=3000$ and $C=3800$ .

$z=\frac{x-u}{s}$ . Find $z$ if $x=22,u=30$ , and $s=8$ .

$-1$

$P=n\left(n-1\right)\left(n-2\right)$ . Find $P$ if $n=-3$ .

## Negative exponents ( [link] )

Write the expressions for the following problems using only positive exponents.

${a}^{-1}$

$\frac{1}{a}$

${c}^{-6}$

${a}^{3}{b}^{-2}{c}^{-5}$

$\frac{{a}^{3}}{{b}^{2}{c}^{5}}$

${\left(x+5\right)}^{-2}$

${x}^{3}{y}^{2}{\left(x-3\right)}^{-7}$

$\frac{{x}^{3}{y}^{2}}{{\left(x-3\right)}^{7}}$

${4}^{-2}{a}^{-3}{b}^{-4}{c}^{5}$

${2}^{-1}{x}^{-1}$

$\frac{1}{2x}$

${\left(2x+9\right)}^{-3}7{x}^{4}{y}^{-5}{z}^{-2}{\left(3x-1\right)}^{2}{\left(2x+5\right)}^{-1}$

${\left(-2\right)}^{-1}$

$\frac{1}{-2}$

$\frac{1}{{x}^{-4}}$

$\frac{7x}{{y}^{-3}{z}^{-2}}$

$7x{y}^{3}{z}^{2}$

$\frac{4{c}^{-2}}{{b}^{-6}}$

$\frac{{3}^{-2}{a}^{-5}{b}^{-9}{c}^{2}}{{x}^{2}{y}^{-4}{z}^{-1}}$

$\frac{{c}^{2}{y}^{4}z}{9{a}^{5}{b}^{9}{x}^{2}}$

$\frac{{\left(z-6\right)}^{-2}}{{\left(z+6\right)}^{-4}}$

$\frac{16{a}^{5}{b}^{-2}}{-2{a}^{3}{b}^{-5}}$

$-8{a}^{2}{b}^{3}$

$\frac{-44{x}^{3}{y}^{-6}{z}^{-8}}{-11{x}^{-2}{y}^{-7}{z}^{-8}}$

${8}^{-2}$

$\frac{1}{64}$

${9}^{-1}$

${2}^{-5}$

$\frac{1}{32}$

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

${\left({a}^{2}b\right)}^{-3}$

$\frac{1}{{a}^{6}{b}^{3}}$

${\left({x}^{-2}\right)}^{-4}$

${\left({c}^{-1}\right)}^{-4}$

${c}^{4}$

${\left({y}^{-1}\right)}^{-1}$

${\left({x}^{3}{y}^{-4}{z}^{-2}\right)}^{-6}$

$\frac{{y}^{24}{z}^{12}}{{x}^{18}}$

${\left(\frac{{x}^{-6}}{{y}^{-2}}\right)}^{-5}$

${\left(\frac{2{b}^{-7}{c}^{-8}{d}^{4}}{{x}^{-2}{y}^{3}z}\right)}^{-4}$

$\frac{{b}^{28}{c}^{32}{y}^{12}{z}^{4}}{16{d}^{16}{x}^{8}}$

## Scientific notation ( [link] )

Write the following problems using scientific notation.

8739

73567

$7.3567×{10}^{4}$

21,000

746,000

$7.46×{10}^{5}$

8866846

$0.0387$

$3.87×{10}^{-2}$

$0.0097$

$0.376$

$3.76×{10}^{-1}$

$0.0000024$

$0.000000000000537$

$5.37×{10}^{-13}$

46,000,000,000,000,000

Convert the following problems from scientific form to standard form.

$3.87×{10}^{5}$

$387,000$

$4.145×{10}^{4}$

$6.009×{10}^{7}$

$60,090,000$

$1.80067×{10}^{6}$

$3.88×{10}^{-5}$

$0.0000388$

$4.116×{10}^{-2}$

$8.002×{10}^{-12}$

$0.000000000008002$

$7.36490×{10}^{-14}$

$2.101×{10}^{15}$

$2,101,000,000,000,000$

$6.7202×{10}^{26}$

$1×{10}^{6}$

$1,000,000$

$1×{10}^{7}$

$1×{10}^{9}$

$1,000,000,000$

Find the product for the following problems. Write the result in scientific notation.

$\left(1×{10}^{5}\right)\left(2×{10}^{3}\right)$

$\left(3×{10}^{6}\right)\left(7×{10}^{7}\right)$

$2.1×{10}^{14}$

$\left(2×{10}^{14}\right)\left(8×{10}^{19}\right)$

$\left(9×{10}^{2}\right)\left(3×{10}^{75}\right)$

$2.7×{10}^{78}$

$\left(1×{10}^{4}\right)\left(1×{10}^{5}\right)$

$\left(8×{10}^{-3}\right)\left(3×{10}^{-6}\right)$

$2.4×{10}^{-8}$

$\left(9×{10}^{-5}\right)\left(2×{10}^{-1}\right)$

$\left(3×{10}^{-2}\right)\left(7×{10}^{2}\right)$

$2.1×{10}^{1}$

$\left(7.3×{10}^{4}\right)\left(2.1×{10}^{-8}\right)$

$\left(1.06×{10}^{-16}\right)\left(2.815×{10}^{-12}\right)$

$2.9839×{10}^{-28}$

$\left(9.3806×{10}^{52}\right)\left(1.009×{10}^{-31}\right)$

what are cluster A disease?
because psychology is a natural science as well as a science. it's a interdisciplinary subject
yes absolutely we cabt out Psychology completely into science dur to its various measuring aspects
utkarsh
cannot* put*
utkarsh
Assess the relationship between heredity and environment in human development
जिवन कक्षा विकासाच्या एकूण किती अवस्था आहेत
what happened Digambar?
sakshi
?
Reina
Is here anybody exactly awared about the medicine used for the schizophrenia?
Fazil
plz can i know if io psychology in demand ou it's better to continu in human resourses management?
Reina
there are many drugs used to alleviate the symptoms, but none are used for curing the disorder itself.
Rupert
Researchers believe that one important function of sleep is to facilitate learning and memory. How does knowing this help you in your college studies? What changes could you make to your study and sleep habits to maximize your mastery of the material covered in class?
Well, for starters, both are entirely different aspect for consideration. As a college student, having an adequate amount of sleep is relatively rare especially on instances where we are totally forced to stay all night (whether for studying or doing academic works).
Rupert
benefits of physcology
who define first physcology
Irfan
who define first physcology
Irfan
I think it was either Henry James Or William James are the father of psychology.
James
I haven't read the flash cards and memorized them sense 2015.
James
so iv forgotten some info and some has never left me . I'm very passionate about psychology.
James
I study medical psychology
John
the history of psychology usually traces back to ancient chinese practices. but modern times acknowledge Wilhelm Wundt as the first person to establish a school.of thought in psychology.
Rupert
huh
ANGELICA
is it wrong?
Rupert
please can i know what is the difference about io psychology and human resources managment and which is more in demand ?
What is psychology
someone who can observe or understand a person's reactions.
Leanne
It is the scientific study of behavior and mental processes
Enos
Sarah is a 30 year old white female. Her occupation is part time chef. She is recently been divorced and has custody of her three children. She has extreme changes in her mood that began to appear in her 20’s but she never went to see a doctor about them. When family tries to talk to her about her u
listen very carefully for red flags on both sides
Leanne
what does historical racism mean
Means that racism was present in a group of peoples race in there past and maybe even now. Example is the Native Americans and African Americans also Asian people. Anyone of not caucasian resent. So people who are mixed races also experience rascism.
James
racism meaning I would believe is a negative impact on other separate cultures, causing some serious concerns to the human race.
Leanne
How do counsel someone that is kinda depressed, lonely and stuffs but the person is pushing you away with by saying stuffs you don't like? Your age mate
let them figure themselves out met them come to you and listen more than speak
Jascelyn
don't take anything too personal someone who is depressed has more feelings other than being sad. I have been through it we dont alwaya mean the things we say. just give time and space but be there when they are ready.
Deanna
the person should be first dealt with very patience and understanding.......... person's trust should be won first to treat that kind of state if counsel is the priority..... don't rush small steps will lead to get successful results....... after the patient start trusting you conversate with them.
Amisha
OK..... Thank you very much It makes me look desperate for the person's attention Thanks tho
Ajayi
just let them know even if they aren't ready to tall right now, you will be here for them whenever they are.
Deanna
we need to wait till the stage comes when he/ she is ready at mental level to participate as he is the subject and the core of the part of that particular conscelling session
aaqib
A.Are they saying it in general manner or B.they are saying it cz they know something about you personally If it is A. then remember it's a part of counseling...even if you don't agree with their views..it is theirs.. so don't take it personally
PREETI
if it is B. tell them .. we are here to talk about them not you Also remember people takes time with things.. so it does get difficult at times.. but in counseling it's about them not you. And if it affecting you much .. see why is there .. and try to objective about it OR refer them to someone
PREETI
allow them time to always become comfortable by listening to all sorts of thoughts they all sound scattered but if you ,just let it go until their ready to ask for advice ,my thoughts of counciling would go for a few more sessions of them venting until they've had enough to feel they want geedback
Leanne
what is the trait in the given example?
what's the given example?
SamieMike
my fat cock
Andrea
o.o u seem like u need to read this txt
SamieMike
learning to understand psychological effects of one's mind thoughts
Leanne
mental state and behavior
Feared ,lethargic, self isolated...
Leanne
because psychology basic is observation asa well as science, so people might skeptical about these two but if we look into it people might notice that it's different because psychology is study about mind and science is study about many thing around us and it's not study about mind clearly.
empirical method is the method of observation on object rather than do experiment .
Karona
ology is the study of theory .
Karona
psyche means soul as well as butterfly.
Karona
psychology is the the study of mind and behavior
Karona
this is where I'm a little sceptical. we learning psychology based on books. but we ourselves r also human. when we to encounter a real life situation how well can we act accordingly
Aileen
im curious more of myself then others
Aileen
psychology is the scientific study of mind and behavior. scientific mean it's based on observation and experiments. yeah we can observe behavior easily but can't read mind directly that's why we do observe behavior and apply test and therapies to study mind basically we behave according to our mind
Faiza
educates a humans thoughts to expand and explore more of how far a mind will go if allowed
Leanne
wilhelm wundt studied psychology for the purpose of
i dont know, all inknow is that he pioneered the practice of introspective and his school of thought aims to study behavior as structured elements
Rupert
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