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Math Help - Indices question!

  1. #1
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    Question Indices question!

    Given that 10^{2n} \times 5^{4-3n} = 2^x \times 5^y, express y in terms of n.

    Answer: x = 2n, y = 4 - n
    I don't know how to begin, how do I get two answers from one given expression? Sorry if I sound dumb but any help will be greatly appreciated! Thanks in advance.
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  2. #2
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    10^{2n} \cdot 5^{4-3n} = 2^x \cdot 5^y

    (2 \cdot 5)^{2n} \cdot 5^{4-3n} = 2^x \cdot 5^y

    2^{2n} \cdot 5^{2n} \cdot 5^{4-3n} = 2^x \cdot 5^y

    2^{2n} \cdot 5^{4-n} = 2^x \cdot 5^y

    finish up by equating exponents
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  3. #3
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    Oh thank you very much skeeter! I haven't really done this sort of sum for a while so I completely forgot about that. Oops.
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  4. #4
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    Note that is m and n could be any numbers, there would be an infinite number of solutions. This problem is assuming that m and n are positive integers.
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  5. #5
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    Hi im stuck on a question, anyone can help?
    simplify
    9^-1/2 x 8^2/3
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  6. #6
    Senior Member eumyang's Avatar
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    (Removed as author of post #5 started a new thread.)
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