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Math Help - Algebra and Functions

  1. #1
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    Algebra and Functions

    Hi I have just done my first day doing A levels. My teacher has given me homework to do with simplifying and evaluating expressions. I don't understand the method on how to solve the equation.

    An example of one of the simplifying questions is: 5x^(1+2/5) / x^(2/5)

    An example of one of the evaluation questions is: 27/8^(2/3)

    My apologies for not using the LaTeX software but I tried for about half an hour to input the equation correctly but only got errors.
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  2. #2
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    Re: Algebra and Functions

    Quote Originally Posted by jacobjacob44 View Post
    Hi I have just done my first day doing A levels. My teacher has given me homework to do with simplifying and evaluating expressions. I don't understand the method on how to solve the equation.

    An example of one of the simplifying questions is: 5x^(1+2/5) / x^(2/5)

    An example of one of the evaluation questions is: 27/8^(2/3)

    My apologies for not using the LaTeX software but I tried for about half an hour to input the equation correctly but only got errors.
    The first one, use \displaystyle \frac{a^m}{a^n} = a^{m - n}.

    The second one, \displaystyle 8^{\frac{2}{3}} = \left(8^{\frac{1}{3}\right)^2 = \left(\sqrt[3]{8}\right)^2...
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  3. #3
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    Re: Algebra and Functions

    what you will do when the problem is X^3/ X^2. same logic.
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  4. #4
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    Re: Algebra and Functions

    Thanks for the first one that has worked great.

    As for the second one I have realised I made a mistake. I didnt mean for it to look like 27 divided by 8 ^ 2/3.
    I meant for it to look like (\frac{27}{8})^\frac{2}{3}
    Still learning on how to work the software.
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  5. #5
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    Re: Algebra and Functions

    Quote Originally Posted by jacobjacob44 View Post
    Thanks for the first one that has worked great.

    As for the second one I have realised I made a mistake. I didnt mean for it to look like 27 divided by 8 ^ 2/3.
    I meant for it to look like (\frac{27}{8})^\frac{2}{3}
    Still learning on how to work the software.
    You should know that \displaystyle \left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}...
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  6. #6
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    Re: Algebra and Functions

    I'll get you started:

    (\frac{27}{8})^{\frac{2}{3}}=\frac{27^{2/3}}{8^{2/3}}
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  7. #7
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    Re: Algebra and Functions

    Okay, I understand the working behind what you have both said. What is confusing me however is in the notes I took from what my teacher did in class included square and cube roots e.g an example she gave us:
    (\frac{64}{81})^\frac{1}{2} = \sqrt{\frac{64}{81}} = \frac{\sqrt{64}}{\sqrt{81}} = \frac{8}{9}
    Sorry if this is something obvious that I am not getting, just its all very confusing for me at the moment
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  8. #8
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    Re: Algebra and Functions

    if a term is raised to the 1/2 power , that is equivalent to the square root of that term.

    the square root of a fraction is equivalent to the square root of the numerator divided by the square root of the denominator.
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  9. #9
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    Re: Algebra and Functions

    Okay, so would the way to work out my original question (\frac{27}{8})^\frac{2}{3} work out something like this?


    (\frac{27}{8})^\frac{2}{3} = \frac{27^{2/3}}{8^{2/3}} = \frac{3}{2}

    3 being the cube root of 27 and 2 being the cube root of 8?
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  10. #10
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    Re: Algebra and Functions

    Quote Originally Posted by jacobjacob44 View Post
    Okay, so would the way to work out my original question (\frac{27}{8})^\frac{2}{3} work out something like this?


    (\frac{27}{8})^\frac{2}{3} = \frac{27^{2/3}}{8^{2/3}} = \frac{3}{2}

    3 being the cube root of 27 and 2 being the cube root of 8?
    Almost there. Now you need to square each term, since it's to the power of 2/3, not 1/3.
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  11. #11
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    Re: Algebra and Functions

    Ahh I see! So would that make the final answer be \frac{9}{6}?
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  12. #12
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    Re: Algebra and Functions

    Quote Originally Posted by jacobjacob44 View Post
    Ahh I see! So would that make the final answer be \frac{9}{6}?
    Is 2^2 = 6?
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  13. #13
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    Re: Algebra and Functions

    apologies, \frac{9}{4}
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  14. #14
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    Re: Algebra and Functions

    Quote Originally Posted by jacobjacob44 View Post
    apologies, \frac{9}{4}
    you got it!
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  15. #15
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    Re: Algebra and Functions

    Thanks for all of the help.
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