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Math Help - law of indices problem

  1. #1
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    law of indices problem

    Hi

    The name is Chris, I am the father of a boy in year 11. My maths classes were many years ago and I only ever got to year 10

    Can you help me help him?

    he has the following problem

    9x+1/32x-1 find to the power of 3

    Now I know the answer is 33 but I need to understand the steps to get to it
    That way I can work through it with him

    I know it must be simple as wolframalpha doesnt even bother showing the steps

    Thanks in advance
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  2. #2
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    Re: law of indices problem

    Hey CuriousChris.

    The basic reason is that 3^2 = 9 and power laws work in that (x^a)^b = x^(ab) so if you let x = 3 a = 2 and b = x+1 then (3^2)^(x+1) = 3^(2(x+1)) = 3^(2x+1) = 9^(x+1).

    So if 3^(2x+2)/3^(2x-1) using exponent laws if you divide you subtract the bottom index from the top to get 3^(2x+2 - (2x-1)) = 3^(2+1) = 3^3.
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  3. #3
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    Re: law of indices problem

    In problems like this you have to make the bases the same so the 9 becomes 3^2 giving
    3^(2x + 2) / 3^(2x - 1) then like chiro says using the second law of indices division become subtraction (when the bases match) giving

    3^(2x + 2) - (2x - 1) = 3^(2 + 1) = 3^3 = 27.

    Good luck.
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  4. #4
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    Re: law of indices problem

    Hi Guys this is my third attempt to reply. Sorry I keep getting dragged away.

    Thanks for your invaluable assistance.

    I will remind my son when dealing with such problems to try to get all bases the same if possible. Then to think of the laws of indices and see which apply.

    Thanks again. you'll probably see a lot more of me over the next year as my son does year 12

    CC
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  5. #5
    Forum Admin topsquark's Avatar
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    Re: law of indices problem

    We welcome him or you any time at all.

    -Dan
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