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Math Help - neg. exponents and fractions

  1. #1
    Newbie
    Joined
    Oct 2009
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    23

    neg. exponents and fractions

    There are 3 problems I am having issues with due to order of operations and negative exponents/fractions:

    (2x(x + 6)^4) − (4x^2(x + 6)^3)


    (x^-1(2 − x^2)) + (x^-2(2 − x^2)^2)


    (7-3x)^(2/3) + 3/2x(7-3x)^-(1/3)

    Help of any sort would be nice. Solutions are cool so I can work through it to figure out how to get the answer, or hints on steps to take are awesome too.

    Appreciate it, guys, you are awesome.
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  2. #2
    Super Member

    Joined
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    Lexington, MA (USA)
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    Hello, shiznid12!

    Here's the third one . . .


    (7-3x)^{\frac{2}{3}} + \tfrac{3}{2}x(7-3x)^{-\frac{1}{3}}

    We have: . (7-3x)^{\frac{2}{3}} + \frac{3x}{2(7-3x)^{\frac{1}{3}}}


    Get a common denominator:

    . . \frac{(7-3x)^{\frac{2}{3}}}{1}\cdot{\color{blue}\frac{2(7-3x)^{\frac{1}{3}}}{2(7-3x)^{\frac{1}{3}}}} \:+\: \frac{3x}{2(7-3x)^{\frac{1}{3}}} . =\;\;\frac{2(7-3x)}{2(7-3x)^{\frac{1}{3}}} + \frac{3x}{2(7-3x)^{\frac{1}{3}}}


    . . . =\;\; \frac{2(7-3x) + 3x}{2(7-3x)^{\frac{1}{3}}} \;\;=\;\;\frac{14 - 6x + 3x}{2(7-3x)^{\frac{1}{3}}} \;\;=\;\;\boxed{ \frac{14-3x}{2(7-3x)^{\frac{1}{3}}}}

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