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Math Help - An algebra question

  1. #1
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    An algebra question

    Question: Simplify the following expression.

    (2x5^n)^2 + 25^n

    this whole equation is divided by

    5^n



    Answer; 5^n+1


    Remarks: I have tried doing this question twice but both attempts were unsuccesful. Please help.
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  2. #2
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    Quote Originally Posted by econlover View Post
    Question: Simplify the following expression.

    (2x5^n)^2 + 25^n

    this whole equation is divided by

    5^n



    Answer; 5^n+1


    Remarks: I have tried doing this question twice but both attempts were unsuccesful. Please help.
    1. Use the laws of powers:

    \frac{(2 \cdot 5^n)^2 + 25^n}{5^n} = \frac{4 \cdot 5^{2n} + 5^{2n}}{5^n}= \frac{5 \cdot 5^{2n}}{5^n}=5 \cdot 5^n = 5^{n+1}
    Last edited by earboth; June 19th 2010 at 07:34 AM.
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  3. #3
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    slight question

    Thanks.

    I understand most of it but how did you move along from the 1st step of your answer to the second one

    that is, in specific terms, where did the 4 go?
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  4. #4
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    considering the numerator (top of fraction) only:
     4 . 5^{2n} + 5^{2n} = (4+1).5^{2n} = 5 \times 5^{2n} = 5^{2n+1}
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  5. #5
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    Thanks for the message. But I guess you misinterpret the sign of this "."

    It is not 4.5 (4 decimal 5) but 4 . 5 meaning 4 x 5 = 4 times 5

    Hope this clears up the misconception
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  6. #6
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    Still don't understand this step. Where did the 1 come from ? What about the positive sign?

    Can someone explain? Thanks!
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  7. #7
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    it is only factorising. i was not interpreting your dot as a decimal.

    in general:
    4x + x = (4+1)x = 5x


    You have
    4 \times 5^{2n} + 1 \times 5^{2n} = 5 \times 5^{2n}

    Which says: "4 lots of 5^{2n} plus 1 lot of  5^{2n}" equals "5 lots of 5^{2n}"
    Last edited by SpringFan25; June 16th 2010 at 01:13 PM.
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  8. #8
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    Quote Originally Posted by econlover View Post
    Question: Simplify the following expression.

    (2x5^n)^2 + 25^n

    this whole equation is divided by

    5^n



    Answer; 5^n+1


    Remarks: I have tried doing this question twice but both attempts were unsuccesful. Please help.
    Hi ecolover,
    answer is correct 5^n+1

    follow exp rules carefully. the 4 disappears naturally because 4+1 =5 You should get it from this clue

    bjh
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