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Math Help - Fractional Indices

  1. #1
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    Fractional Indices

    4n^{3/2} = 8^{-1/3}

    Find the value of n

    hi all, ive been given the above and need to solve it without a calculator. ive expessed it in all the indice rules but cant come up with a suitable format to solve it.

    any ideas?

    here's what i got so far n^{3/2} = \frac{1}{8}
    so does n = \sqrt[{3/2}]{1/8}

    thanks for the model answer ADARSH and help with formatting

    (n^{3/2})^{2/3}=(2^{-3})^{2/3}
    therefore
    n=2^{-2}
    therefore
    n=\frac{1}{2^2}
    Last edited by sammy28; February 24th 2009 at 09:54 AM.
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  2. #2
    Like a stone-audioslave ADARSH's Avatar
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    Welcome to the Forum


    4 = 2^2

    8 = 2^3

    using it in
    4n^{3/2} = 8^{-1/3}

    we get
    2^2 n^{3/2} = (2^{3})^{-1/3}

    divide both sides by 2^2

    n^{3/2} = \frac {2^{-1}  }{2^2}

    Thus
    n^{3/2} = 2^{-1 - 2}

    Hence

    n^{3/2} = 2^{-3}

    This can be written as

    (n^{3/2})^{2/3} = (2^{-3})^{2/3}

    Hence

     <br />
n^1 = \frac{1}{2^{(2*3)/3}}<br />

    Hence n= \frac{1}{4}
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  3. #3
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    wow thanks for taking the time to look at that one. i thought id covered them all except i didnt think about converting 2 to the power of n as a first step. and multiplying by the reciprocal.

    now i can do it without a calculator

    thanks for the welcome too. how can you format questions like your answer, ie using mathematical symbols?
    Last edited by sammy28; February 24th 2009 at 07:16 AM.
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  4. #4
    Like a stone-audioslave ADARSH's Avatar
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    Its really good that you have asked about it ...Inorder to format

    your questions lke that Read this thread and the attatched pdf
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