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Math Help - GMAT question

  1. #1
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    GMAT question

    I put this one under the high school level because it really shouldn't be that hard, but it has me stumped. Any advice?

    Question: what is the value of m in the following expression?

    (1/5)^m * (1/4)^18 = 1/(2*(10^35))

    The denominator exponent bases on the LHS are 5 and 4, so they can't be combined. I was thinking about 4 = 2^2, but that isn't helping me either.

    Anything thoughts are much appreciated.
    --integrity
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  2. #2
    Junior Member mathfun's Avatar
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    $${\left( {\tfrac{1}{5}} \right)^m} \cdot {\left( {\tfrac{1}{4}} \right)^{18}} = \tfrac{1}{2} \cdot {10^{ - 35}} \Leftrightarrow {\left( {\tfrac{1}{5}} \right)^m} = \tfrac{1}{2}{\left( {\tfrac{1}{2}} \right)^{ - 36}}{10^{ - 35}} \Leftrightarrow {\left( {\tfrac{1}{5}} \right)^m} = {\left( {\tfrac{1}{5}} \right)^{35}} \Leftrightarrow m = 35$$
    Last edited by mathfun; March 26th 2011 at 11:13 AM. Reason: Correction
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  3. #3
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    Thanks for your quick response mathfun. Much appreciated!
    I went through your calculations carefully and I think a negative sign was dropped in the 4th step, which would mean the correct answer is ultimately 35. I think.
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  4. #4
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    Hello, integrity!

    \displaystyle \text{Solve for }m:\;\left(\frac{1}{5}\right)^m\left(\frac{1}{4}\r  ight)^{18} \:=\:\frac{1}{2\cdot10^{35}}

    \text{I did it like this . . .}


    \displaystyle\text{We have: }\:\frac{1}{5^m}\cdot\frac{1}{(2^2)^{18}} \;=\;\frac{1}{2\cdot(2\cdot5)^{35}}

    . . . . . . . . . . \displaystyle \frac{1}{5^m}\cdot\frac{1}{2^{36}} \;=\;\frac{1}{2\cdot2^{35}\cdot5^{35}}

    . . . . . . . . . . \displaystyle \frac{1}{5^m\cdot2^{36}} \;=\;\frac{1}{2^{36}\cdot5^{35}}

    \displaystyle \text{Multiply by }2^{36}\!:\;\;\frac{1}{5^m} \;=\;\frac{1}{5^{35}}

    . . . . . . . . . . . . . \displaystyle 5^{-m} \;=\;5^{-35}

    . . . . . . . . . . . . . -m \;=\;-35

    . . . . . . . . . . . . . . m \;=\;35

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  5. #5
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    That's it! Thanks very much.
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