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1/(x^4) = 4^4 simplifies to 1/x = 4

  1. Dec 29, 2012 #1
    Quick math question: Why does 1/(x^4) = 4^4 simplify to 1/x = 4?
     
  2. jcsd
  3. Dec 29, 2012 #2

    micromass

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    It doesn't. It simplifies to

    [tex]1/x=4~\text{or}~1/x=-4[/tex]

    (assuming x is a real number)
     
  4. Dec 29, 2012 #3
    I don't understand why the exponents are disregarded.
     
  5. Dec 29, 2012 #4
    They're not. Take the fourth root of each side.
     
  6. Dec 29, 2012 #5

    symbolipoint

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    [itex]\frac{1}{x^4}=(\frac{1}{x})^4[/itex]
    [itex]\sqrt{(\frac{1}{x})^4}=\pm(\frac{1}{x})^2 [/itex]

    [itex]\sqrt{(\frac{1}{x})^2}=\pm\frac{1}{x} [/itex]
     
    Last edited by a moderator: Jan 2, 2013
  7. Dec 29, 2012 #6

    symbolipoint

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    That's what I am trying to show but typesetting is not working.
     
  8. Dec 29, 2012 #7
    Thanks.
     
  9. Dec 29, 2012 #8

    dextercioby

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    Fixed.
     
  10. Dec 29, 2012 #9

    symbolipoint

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    Thanks. Now by comparison of the tex code I can see my parenthesis mistake in one of them.
     
  11. Dec 30, 2012 #10

    Char. Limit

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    Are we assuming x is real here? Because there's two other possibilities for x that yield the same answer.
     
  12. Dec 30, 2012 #11
    [itex]x^{-4} = 4^{4}[/itex]
     
  13. Dec 30, 2012 #12

    dextercioby

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    And even better:

    [tex] x^{-4} = \left(\frac{1}{4}\right)^{-4} [/tex] :tongue2:
     
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