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Homework Help: Laws of exponants

  1. Jun 13, 2013 #1

    reenmachine

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    Gold Member

    1. The problem statement, all variables and given/known data

    Simplify the following expression:

    ##\frac{(100^3)^\frac{2}{3}}{1000^\frac{1}{3}}## ÷ ##\left( \frac{-10^2}{100^\frac{1}{2}} \right)^3##


    2. Relevant equations

    Start with this side: ##\frac{(100^3)^\frac{2}{3}}{1000^\frac{1}{3}}##

    ##\frac{((10^2)^3)^\frac{2}{3}}{(10^3)^\frac{1}{3}}##

    ##\frac{(10^6)^\frac{2}{3}}{10}##

    ##\frac{10^4}{10}##

    ##10^3##

    We keep this and go on the right side of the expression:

    ##\left( \frac{-10^2}{100^\frac{1}{2}} \right)^3##

    ##\left( \frac{-10^2}{(10^2)\frac{1}{2}} \right)^3##

    ##\left( \frac{-10^2}{10} \right)^3##

    ##\left( \frac{-10^6}{10^3} \right)##

    ##-10^3##

    Then we take the two results:

    ##\frac{10^3}{-10^3}##

    ##-1##

    Is that a correct way to use the laws of exponants?

    thank you!
     
    Last edited: Jun 13, 2013
  2. jcsd
  3. Jun 13, 2013 #2

    Dick

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    Science Advisor
    Homework Helper

    Looks fine to me.
     
  4. Jun 13, 2013 #3

    reenmachine

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    Gold Member

    thank you!
     
  5. Jun 14, 2013 #4

    Mark44

    Staff: Mentor

    Minor point: the word is exponent.
     
  6. Jun 14, 2013 #5

    reenmachine

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    Gold Member

    Oops , in french it's "exposant" , that's probably where the confusion came from.

    Thank you!
     
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