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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

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
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
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
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.
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
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
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.
what is the actual application of fullerenes nowadays?
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.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
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.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Mueller 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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