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This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr. The symbols, notations, and properties of numbers that form the basis of algebra, as well as exponents and the rules of exponents, are introduced in this chapter. Each property of real numbers and the rules of exponents are expressed both symbolically and literally. Literal explanations are included because symbolic explanations alone may be difficult for a student to interpret.Objectives of this module: understand exponential notation, be able to read exponential notation, understand how to use exponential notation with the order of operations.

Overview

  • Exponential Notation
  • Reading Exponential Notation
  • The Order of Operations

Exponential notation

In Section [link] we were reminded that multiplication is a description for repeated addition. A natural question is “Is there a description for repeated multiplication?” The answer is yes. The notation that describes repeated multiplication is exponential notation .

Factors

In multiplication, the numbers being multiplied together are called factors . In repeated multiplication, all the factors are the same. In nonrepeated multiplication, none of the factors are the same. For example,

18 18 18 18 Repeated multiplication of 18. All four factors , 18 , are the same . x x x x x Repeated multiplication of x . All five factors , x , are the same . 3 7 a Nonrepeated multiplication . None of the factors are the same .

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Exponential notation is used to show repeated multiplication of the same factor. The notation consists of using a superscript on the factor that is repeated . The superscript is called an exponent .

Exponential notation

If x is any real number and n is a natural number, then

x n = x x x ... x n factors of x

An exponent records the number of identical factors in a multiplication.

Note that the definition for exponential notation only has meaning for natural number exponents. We will extend this notation to include other numbers as exponents later.

Sample set a

7 7 7 7 7 7 = 7 6 .

The repeated factor is 7. The exponent 6 records the fact that 7 appears 6 times in the multiplication.

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x x x x = x 4 .

The repeated factor is x . The exponent 4 records the fact that x appears 4 times in the multiplication.

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( 2 y ) ( 2 y ) ( 2 y ) = ( 2 y ) 3 .

The repeated factor is 2 y . The exponent 3 records the fact that the factor 2 y appears 3 times in the multiplication.

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2 y y y = 2 y 3 .

The repeated factor is y . The exponent 3 records the fact that the factor y appears 3 times in the multiplication.

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( a + b ) ( a + b ) ( a b ) ( a b ) ( a b ) = ( a + b ) 2 ( a b ) 3 .

The repeated factors are ( a + b ) and ( a b ) , ( a + b ) appearing 2 times and ( a b ) appearing 3 times.

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Practice set a

Write each of the following using exponents.

( 3 b ) ( 3 b ) ( 5 c ) ( 5 c ) ( 5 c ) ( 5 c )

( 3 b ) 2 ( 5 c ) 4

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2 2 7 7 7 ( a 4 ) ( a 4 )

2 2 7 3 ( a 4 ) 2

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8 x x x y z z z z z

8 x 3 y z 5

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Caution

It is extremely important to realize and remember that an exponent applies only to the factor to which it is directly connected.

Sample set b

8 x 3 means 8 x x x and not 8 x 8 x 8 x . The exponent 3 applies only to the factor x since it is only to the factor x that the 3 is connected.

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Questions & Answers

what is variations in raman spectra for nanomaterials
Jyoti Reply
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
yes that's correct
Professor
I think
Professor
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 did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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