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

1. ## 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!

2. ## Re: Help with simplifying fraction with a negative exponent.Unsure of final result st

We have:

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

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

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

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

So we have:

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

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

There are two ways to view the next step:

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

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

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

And then you can make the substitution.

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

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

Either way, we are left with:

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

And we want to substitute in:

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

Which we can now do, leaving:

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