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

We have come up with the following definitions.

  • x 0 1
  • x a = 1 x a size 12{ { {1} over {x rSup { size 8{a} } } } } {}
  • x a b = x a b size 12{ nroot { size 8{b} } {x rSup { size 8{a} } } } {}

Let’s get a bit of practice using these definitions.

Check all of your answers above on your calculator. If any of them did not come out right, figure out what went wrong, and fix it!

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Solve for x : x x size 12{ { {x rSup { size 8{ {3} wideslash {2} } } } over {x rSup { size 8{ {1} wideslash {2} } } } } } {} 17 1 2 17 1 2

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Simplify: x x size 12{ { {x} over { sqrt {x} } } } {}

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Simplify: x + x x + 1 x size 12{ { {x rSup { size 8{ {3} wideslash {2} } } + sqrt {x} } over {x rSup { size 8{ {5} wideslash {2} } } + { {1} over { sqrt {x} } } } } } {}

Multiply the top and bottom by x 1 2 .
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Now…remember inverse functions? You find them by switching the x and the y and then solving for y . Find the inverse of each of the following functions. To do this, in some cases, you will have to rewrite the things. For instance, in #9, you will start by writing y x 1 2 . Switch the x and the y , and you get x y 1 2 . Now what? Well, remember what that means: it means x y . Once you’ve done that, you can solve for y , right?

x 3

  • Find the inverse function.
  • Test it.
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x -2

  • Find the inverse function.
  • Test it.
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x 0

  • Find the inverse function.
  • Test it.
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Can you find a generalization about the inverse function of an exponent?

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Graph y 2 x by plotting points. Make sure to include both positive and negative x values.

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Graph y 2 2 x by doubling all the y-values in the graph of y 2 x .

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Graph y 2 x 1 by taking the graph y 2 x and “shifting” it to the left by one.

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Graph y 1 2 x by plotting points. Make sure to include both positive and negative x values.

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Questions & Answers

how do you translate this in Algebraic Expressions
linda Reply
why surface tension is zero at critical temperature
Shanjida
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
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Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
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
Azam
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
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
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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