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Math Help - EXPONENTS AND ROOTS What is the m root of (16^2m + 64^m) /(8^m + 32^m)?

  1. #1
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    Question EXPONENTS AND ROOTS What is the m root of (16^2m + 64^m) /(8^m + 32^m)?

    Sorry, I'm not good with notations, if you can't understand this: the m root of (16^2m + 64^m) /(8^m + 32^m)

    Here's an image of the equation:

    EXPONENTS AND ROOTS What is the m root of (16^2m + 64^m) /(8^m + 32^m)?-math-prob.png

    The answer, according to the book, is 8, but, unfortunately, it doesn't show the solution. Can you show me why it's 8 please?

    Thanks a lot!
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  2. #2
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    Re: EXPONENTS AND ROOTS What is the m root of (16^2m + 64^m) /(8^m + 32^m)?

    I'll get you started,

    \frac{16^{2m}+64^m}{8^m+32^m}

    =\frac{(2^4)^{2m}+(2^6)^m}{(2^3)^m+(2^5)^m}

    =\frac{2^{8m}+2^{6m}}{2^{3m}+2^{5m}}

    Now factorise..
    Thanks from viccal
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    Re: EXPONENTS AND ROOTS What is the m root of (16^2m + 64^m) /(8^m + 32^m)?

    Quote Originally Posted by a tutor View Post
    I'll get you started,

    \frac{16^{2m}+64^m}{8^m+32^m}

    =\frac{(2^4)^{2m}+(2^6)^m}{(2^3)^m+(2^5)^m}

    =\frac{2^{8m}+2^{6m}}{2^{3m}+2^{5m}}

    Now factorise..
    Actually, that's where I get stuck. I can't get past that point, but good to know I was on the right track
    Last edited by viccal; August 12th 2012 at 01:16 AM.
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  4. #4
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    Re: EXPONENTS AND ROOTS What is the m root of (16^2m + 64^m) /(8^m + 32^m)?

    =\frac{2^{8m}+2^{6m}}{2^{3m}+2^{5m}}

    =\frac{2^{6m}(2^{2m}+1)}{2^{3m}(2^{2m}+1)}=2^{3m}
    Thanks from viccal
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