# 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.

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

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

$2.1×{10}^{14}$

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

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

$2.7×{10}^{78}$

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

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

$2.4×{10}^{-8}$

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

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

$2.1×{10}^{1}$

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

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

$2.9839×{10}^{-28}$

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

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
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
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?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
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
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
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 ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
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
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