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Thread: Help with simplifying fraction with a negative exponent.Unsure of final result steps

  1. #1
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    Help with simplifying fraction with a negative exponent.Unsure of final result steps

    Not sure what happened with the R^-0.67 in getting to the final expression for MP. I understand substituting Gw back into the formula but how does it become (Gw/R). And also the .83 constant becomes .33?

    I would have just brought the R^ -0.67 to the denominator to get a positive exponent.

    Thank you!
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  2. #2
    Super Member Quacky's Avatar
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    Re: Help with simplifying fraction with a negative exponent.Unsure of final result st

    We have:

    $\displaystyle MP^w_r=\frac{0.83A^{0.67}}{R^{0.67}}$

    We want to substitute in $\displaystyle G_w=2.5A^{0.67}R^{0.33}$

    But two things hinder us:
    -The uneven powers of R
    -The unequal constants.

    Some quick division tells us that $\displaystyle 0.83=2.5(0.332)$

    So we have:

    $\displaystyle MP^w_r=\frac{0.83A^{0.67}}{R^{0.67}}$

    $\displaystyle MP^w_r=\frac{0.332(2.5)A^{0.67}}{R^{0.67}}$

    There are two ways to view the next step:

    You could conceptualize it as multiplying through by $\displaystyle \frac{R^{0.33}}{R^{0.33}}$ to give:

    $\displaystyle MP^w_r=\frac{0.332(2.5)A^{0.67}R^{0.33}}{R^{0.67}R ^{0.33}}$

    $\displaystyle MP^w_r=\frac{0.332(2.5)A^{0.67}R^{0.33}}{R^{1}}$

    And then you can make the substitution.

    Or consider the fact that $\displaystyle x^a\cdot{x^b}=x^{a+b}$

    We need $\displaystyle R^{0.33}$ in the numerator.
    We currently have $\displaystyle R^{-0.67}$ in the numerator. You can then deduce that $\displaystyle R^{0.33}R^{-1}=R^{-0.67}$ so we can rewrite $\displaystyle R^{-0.67}$ as $\displaystyle R^{0.33}R^{-1}$

    Either way, we are left with:

    $\displaystyle MP^w_r=\frac{0.332(2.5)A^{0.67}R^{0.33}}{R^{1}}$

    And we want to substitute in:

    $\displaystyle G_w=2.5A^{0.67}R^{0.33}$

    Which we can now do, leaving:

    $\displaystyle MP^w_r=\frac{0.332G_w}{R^{1}}$
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