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Thread: Radicals

  1. #11
    Eliz and pka... thank you both very much. (I'm getting it. I'm gone.) John
    A struggling student.

  2. #12
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    Sooooooo:

    show "radicand of n" this way : sqrt(n)

    3x^2 = 3 times x^2

    (3x)^2 = 9 times x^2

    Mais oui, Jean ?
    I'm just an imagination of your figment !

  3. #13
    pka,
    I did well with your first 2 examples, but the third:
    (-xy^2)^4*(x^3y^2)^3 = (x^4y^8)(x^9y^6) = x^13y^14

    is a puzzle (to me). The first parenthetical term: (-xy^2)^4

    Isn't there an invisible "1" between the minus sign and the "x"? Raising "-1x" to the 4th power looks like (-1x)(-1x)(-1x)(-1x). Does this not require the "Same Sign Rule"... to keep the sign and add the numbers? Result would be (-x^4y^8)

    Did you intentionally throw me a curve, or am I still thick?
    John
    PS A belated thank you, Denis.
    A struggling student.

  4. #14
    Elite Member stapel's Avatar
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    What is (-1)<sup>4</sup>?

    Eliz.

  5. #15
    Eliz,
    Thank you. 1 to the 4th power would be 1. The term is (-1x)^4. What happens to the minus sign?
    John
    A struggling student.

  6. #16
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    Quote Originally Posted by John Whitaker
    The term is (-1x)^4. What happens to the minus sign?

    Mr. Whitaker, you must learn the basic idea.

    [tex]\left( {ab} \right)^n = a^n b^n[/tex] this is true period!
    [tex]\left( { - x} \right)^4 = \left( { - 1x} \right)^4 = \left( { - 1} \right)^4 \left( x \right)^4 = x^4[/tex]

    For any even counting number n , [tex]\left( { - x} \right)^n = x^n[/tex].
    Why? Because n is even, n=2j for some j, so
    [tex]\left( { - x} \right)^n = \left( { - x} \right)^{2j} = \left[ {\left( { - x} \right)^2 } \right]^j = \left( {x^2 } \right)^j = x^{2j} = x^n[/tex]

    Now What happens to the minus sign?
    “A professor is someone who talks in someone else’s sleep”
    W.H. Auden

  7. #17
    Elite Member stapel's Avatar
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    Quote Originally Posted by stapel
    What is (-1)<sup>4</sup>?
    Quote Originally Posted by John Whitaker
    1 to the 4th power would be 1
    Yes, but that doesn't answer my question.

    You are correct that (1)<sup>4</sup> = 1. But what is (-1)<sup>4</sup>?

    Eliz.

  8. #18
    Eliz,
    (-1)^4... That would be "-1"
    If you can see the 3 samples pka gave me, look at the first parenthetical term in the second sample... and the same in the third.
    RE: The second: (-xy^2)^4 If the simplication of that is -x^3y^6, then the simplication of sample #3: (-xy^2)4 should be (-x^4y^8). pka shows it to be: (x^4y^8). This is what I question. What happened to the minus sign in pka's third sample?
    John
    A struggling student.

  9. #19
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    Quote Originally Posted by John Whitaker
    Eliz,
    (-1)^4... That would be "-1"
    If you can see the 3 samples pka gave me, look at the first parenthetical term in the second sample... and the same in the third.
    RE: The second: (-xy^2)^4 If the simplication of that is -x^3y^6, then the simplication of sample #3: (-xy^2)4 should be (-x^4y^8). pka shows it to be: (x^4y^8). This is what I question. What happened to the minus sign in pka's third sample?
    John
    I give up!
    The dragon of confusion has slain George the reasonable!
    “A professor is someone who talks in someone else’s sleep”
    W.H. Auden

  10. #20
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    Quote Originally Posted by pka
    Quote Originally Posted by John Whitaker
    Eliz,
    (-1)^4... That would be "-1"
    If you can see the 3 samples pka gave me, look at the first parenthetical term in the second sample... and the same in the third.
    RE: The second: (-xy^2)^4 If the simplication of that is -x^3y^6, then the simplication of sample #3: (-xy^2)4 should be (-x^4y^8). pka shows it to be: (x^4y^8). This is what I question. What happened to the minus sign in pka's third sample?
    John
    I give up!
    The dragon of confusion has slain George the reasonable!
    You're not alone. I have no either what John is doing or trying to convey to us either.

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