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

  1. Quick math question: Why does 1/(x^4) = 4^4 simplify to 1/x = 4?
     
  2. jcsd
  3. micromass

    micromass 19,689
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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. I don't understand why the exponents are disregarded.
     
  5. They're not. Take the fourth root of each side.
     
  6. symbolipoint

    symbolipoint 3,316
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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. symbolipoint

    symbolipoint 3,316
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    That's what I am trying to show but typesetting is not working.
     
  8. Thanks.
     
  9. dextercioby

    dextercioby 12,324
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    Fixed.
     
  10. symbolipoint

    symbolipoint 3,316
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    Thanks. Now by comparison of the tex code I can see my parenthesis mistake in one of them.
     
  11. Char. Limit

    Char. Limit 1,986
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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. [itex]x^{-4} = 4^{4}[/itex]
     
  13. dextercioby

    dextercioby 12,324
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    And even better:

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