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Math Help - Simplifying radicals

  1. #1
    Junior Member Greymalkin's Avatar
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    Question Simplifying radicals

    Express/simplify as a single log
    [(3/2)ln4x^6]-[(4/5)ln2y^10]


    book answer is 2^(11/5)x^9/y^8
    my answer is (8x^9)/[(16^1/5)y^8]

    I need to simplify 8/[16^(1/5)] to get to 2^(11/5)/1 which equals 2^(11/5)x^9/y^8
    I'm oblivious as to how this is achieved, please help.
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  2. #2
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    Re: Simplifying radicals

    Quote Originally Posted by Greymalkin View Post
    Express/simplify as a single log
    [(3/2)ln4x^6]-[(4/5)ln2y^10]


    book answer is 2^(11/5)x^9/y^8
    my answer is (8x^9)/[(16^1/5)y^8]

    I need to simplify 8/[16^(1/5)] to get to 2^(11/5)/1 which equals 2^(11/5)x^9/y^8
    I'm oblivious as to how this is achieved, please help.
    8/{16^(1/5)}= 2^3/(2^4)^(1/5)=2^3/2^(4/5) =2^(3-4/5)=2^(11/5)
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  3. #3
    MHF Contributor Reckoner's Avatar
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    Re: Simplifying radicals

    The book kept the 8 and 16 as powers of 2:

    \ln\frac{8x^9}{16^{1/5}y^8}

    =\ln\frac{2^3x^9}{2^{4/5}y^8}

    =\ln\frac{2^{3-4/5}x^9}{y^8}

    =\ln\frac{2^{11/5}x^9}{y^8}
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