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Homework Help: Scientific notation root powers exponents question

  1. Jan 17, 2012 #1
    1. The problem statement, all variables and given/known data

    scientific notation

    I have a problem that displays the 4th root of the square root of 5.2 x 10 to the -9th power

    2. Relevant equations

    4 . ............. .... .... -9
    ... sq rt of 5.2 X 10

    Code (Text):


    4                        -9
       sq rt of 5.2 X 10

     
    3. The attempt at a solution

    The answer I get is +- 8.5 x 10 to the negative 3rd power
    but the book is giving me an answer of +- 2.7 x 10 to the -2nd power

    I get the +- because it's an even root which means an absolute or + or - number can be squared.
    I moved the decimal place 3 places to the right so that the power of -12 can be easily divided by the power of 4.
    I tried reversing the decimal place as well so that the power is -8.
    I am not getting why I am not coming up with the same answer as the book. I really believe the book is in error.
    Can anyone verify either of these and please explain what I am doing wrong if I am incorrect?

    Thank you so much in advance.
     
  2. jcsd
  3. Jan 17, 2012 #2

    Mark44

    Staff: Mentor

    Your descriptions are ambiguous. Is this what you mean?
    [tex]\sqrt[4]{\sqrt{5.2~ X~ 10^{-9}}}[/tex]

    Or is it this?
    [tex]\sqrt[4]{\sqrt{5.2}}~X~10^{-9}[/tex]

    In either case, the fourth root of the square root is the eighth root.
     
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