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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 .

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.

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.

( 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.

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.

( 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.

Practice set a

Write each of the following using exponents.

a a a a

a 4

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

( 3 b ) 2 ( 5 c ) 4

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

2 2 7 3 ( a 4 ) 2

8 x x x y z z z z z

8 x 3 y z 5

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.

Questions & Answers

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Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
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. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
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I start with an easy one. carbon nanotubes woven into a long filament like a string
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preparation of nanomaterial
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Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
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AMJAD
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what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
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anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
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name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
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how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
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silver nanoparticles could handle the job?
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this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
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Source:  OpenStax, Basic mathematics review. OpenStax CNX. Jun 06, 2012 Download for free at http://cnx.org/content/col11427/1.2
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