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gabriel72alv

  • 11 months ago

(-3w^3 x^-6)^3 Write your answer using only positive exponents.

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  1. RolyPoly
    • 11 months ago
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    \[x^{-a} = \frac{1}{x^a}\]\[(xy)^m = x^my^m\]

  2. gabriel72alv
    • 11 months ago
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    Please help? I still dont understand? ):

  3. jim_thompson5910
    • 11 months ago
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    how far did you get gabriel72alv?

  4. gabriel72alv
    • 11 months ago
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    I couldnt figure out how to put it in the equation I needed to solve it? ):

  5. jim_thompson5910
    • 11 months ago
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    I'll do a similar example (just with different numbers) \[\Large \left(-2w^{5}x^{-8}\right)^{4}\] \[\Large \left(-2\right)^{4}\left(w^{5}\right)^{4}\left(x^{-8}\right)^{4}\] \[\Large \left((-2)^{1}\right)^{4}\left(w^{5}\right)^{4}\left(x^{-8}\right)^{4}\] \[\Large (-2)^{1*4}w^{5*4}x^{-8*4}\] \[\Large (-2)^{4}w^{20}x^{-32}\] \[\Large (-2)^{4}w^{20}\frac{1}{x^{32}}\] \[\Large 16w^{20}\frac{1}{x^{32}}\] \[\Large \frac{16w^{20}}{x^{32}}\]

  6. gabriel72alv
    • 11 months ago
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    So would I get (-3w^3/x^6)^3 ?

  7. jim_thompson5910
    • 11 months ago
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    Keep going. So far, so good.

  8. gabriel72alv
    • 11 months ago
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    Theres still another step? o:

  9. jim_thompson5910
    • 11 months ago
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    Yes there are more steps.

  10. gabriel72alv
    • 11 months ago
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    How would you work it out to get to the next step though? I understand that.

  11. jim_thompson5910
    • 11 months ago
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    You would apply the outermost exponent to each term inside

  12. jim_thompson5910
    • 11 months ago
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    In other words, you would cube each piece.

  13. gabriel72alv
    • 11 months ago
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    So basically would it be, (-3w^3/x^6) times (-3w^3/x^6) times (-3w^3/x^6) ?

  14. jim_thompson5910
    • 11 months ago
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    Yes pretty much

  15. jim_thompson5910
    • 11 months ago
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    So that explains why, for instance, in the denominator you will have x^6*x^6*x^6 = x^(6+6+6) = x^(18)

  16. jim_thompson5910
    • 11 months ago
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    A shortcut is to use this rule \[\Large (x^m)^n = x^{m*n}\]

  17. gabriel72alv
    • 11 months ago
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    So would I get for my answer to that is -27w^9/x^18 ?

  18. jim_thompson5910
    • 11 months ago
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    You are 100% correct. Nice work.

  19. gabriel72alv
    • 11 months ago
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    Nicee! Haa, So thats my answer? xD

  20. jim_thompson5910
    • 11 months ago
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    Yes it is.

  21. gabriel72alv
    • 11 months ago
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    Awesome, Thank you so much jim_thompson5910 ! (:

  22. jim_thompson5910
    • 11 months ago
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    you're welcome

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