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This module provides sample problems designed to develop concepts related to fractional exponents.

On the homework, we demonstrated the rule of negative exponents by building a table. Now, we’re going to demonstrate it another way—by using the rules of exponents.

  • A

    According to the rules of exponents , 7 3 7 5 size 12{ { {7 rSup { size 8{3} } } over {7 rSup { size 8{5} } } } } {} 7 [ ] .
  • B

    But if you write it out and cancel the excess 7s, then 7 3 7 5 size 12{ { {7 rSup { size 8{3} } } over {7 rSup { size 8{5} } } } } {} = ——.
  • C

    Therefore, since 7 3 7 5 size 12{ { {7 rSup { size 8{3} } } over {7 rSup { size 8{5} } } } } {} can only be one thing, we conclude that these two things must be equal: write that equation!
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Now, we’re going to approach fractional exponents the same way. Based on our rules of exponents , 9 1 2 2 =

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So, what does that tell us about 9 1 2 ? Well, it is some number that when you square it, you get _______ (*same answer you gave for number 2). So therefore, 9 1 2 itself must be:

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Using the same logic, what is 16 1 2 ?

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Construct a similar argument to show that 8 1 2 = 2 .

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What would you expect x 1 5 to be?

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What is 25 1 2 ? (You have to combine the rules for negative and fractional exponents here!)

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Check your answer to #12 on your calculator. Did it come out the way you expected?

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OK, we’ve done negative exponents, and fractional exponents—but always with a 1 in the numerator. What if the numerator is not 1?

Using the rules of exponents, 8 1 3 2 8 [ ] .

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So that gives us a rule! We know what 8 1 2 2 is, so now we know what 8⅔ is.

Construct a similar argument to show what 16 3 4 should be.

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Check 16 3 4 on your calculator. Did it come out the way you predicted?

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Now let’s combine all our rules! For each of the following, say what it means and then say what actual number it is. (For instance, for 9 1 2 you would say it means 9 so it is 3.)

For these problems, just say what it means. (For instance, 3 1 2 means 3 , end of story.)

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, Advanced algebra ii: activities and homework. OpenStax CNX. Sep 15, 2009 Download for free at http://cnx.org/content/col10686/1.5
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