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Exponets messing me up

  1. May 19, 2007 #1
    This is probably a very easy question but it is messing me up.

    (-y^2)^2 = (-y)^4

    but

    (-y^2)^3 = (-y^6)

    why does one exponent need to be inside the brackets and the other outside?

    Example: (-5^2)^2 = 625 = (-5)^4

    (-5^2)^3 = -15625 = (-5^6)
     
  2. jcsd
  3. May 19, 2007 #2

    cristo

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    You really need to move your parentheses to avoid amibiguity; your first line should really read -(y2)2=-(y4)
     
  4. May 19, 2007 #3
    but that would make the answer -625, not 625
     
  5. May 19, 2007 #4

    cristo

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    Sorry, I read it wrong. Well, in that case, you need more parentheses, since -x^2 is very ambiguous; I would take it to mean -(x^2). You should write ((-y)^2)^2, which is equal to (-y)^4, using the correct exponent rule.
     
  6. May 19, 2007 #5
    Ok, so ((-y)^2)^3 = (-y)^6
     
    Last edited: May 19, 2007
  7. May 19, 2007 #6

    cristo

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    Yes. Notice that it is also equal to y^6 if you square the inside bracket first, since (-y)^2=y^2
     
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