# 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 is variations in raman spectra for nanomaterials
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
what is the stm
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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
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what is a peer
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What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
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Rafiq
what is differents between GO and RGO?
Mahi
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Rafiq
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
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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
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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 did you get the value of 2000N.What calculations are needed to arrive at it
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