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Math Help - Req. Help with Fractional Exponent Problem

  1. #1
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    Exclamation Req. Help with Fractional Exponent Problem

    Please tell me what I did wrong.
    This is a question from my review packet.
    The answer says it should be 2 with exponent 3/2

    My attempt gives me this:
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  2. #2
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    Quote Originally Posted by Lovely07 View Post
    Please tell me what I did wrong.
    This is a question from my review packet.
    The answer says it should be 2 with exponent 3/2

    My attempt gives me this:
    Your mistakes are in the third line. You can't just take the exponents out of the square root like that!!

    Note that:

    2^{5/2} = 2^2 \times 2^{1/2} = 4 \sqrt{2} \, and  \, 2^{3/2} = 2^1 \times 2^{1/2} = 2 \sqrt{2}.

    So your problem becomes 4 \sqrt{2} - 2 \sqrt{2} = 2 \sqrt{2}.

    Now note that 2 \sqrt{2} = 2^{3/2}.

    ---------------------------------------------------------------------------

    Alternatively, note that 2^{5/2} = 2^1 \times 2^{3/2} = 2 \times 2^{3/2}.

    So your problem becomes 2 \times 2^{3/2} - 2^{3/2} = 2^{3/2}.
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  3. #3
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    Thank you very much for you help.
    The alternative method was easy to understand.
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