I'm trying to do some exercises of this site, but I'm stuck at the letter r one. Specifically this part $$ \int(...) -\frac{ \sqrt[\leftroot{10} \uproot{1} 6]{x\sqrt[\leftroot{10} \uproot{3} ] {x^{-9}}}} {\sqrt[\leftroot{10} \uproot{3}]{9x\sqrt[\leftroot{10} \uproot{3} ] {x^{10}}}}$$ Simplifying the numerator I got: $$x^{-7/12}$$ The donominator: $$9x^3$$ So I, now I thing we just need to subtract the bottom's exponent from the top's right? $$\frac{-7}{12} - 3 = \frac{-7 - 36}{12}= \frac{-43}{12}$$
Basically we got: $$\frac{x^{-43/12}}{9}$$
Now the reverse power rule, I already added one to the exponent: $$\frac{x^{-31/12}}{9}\frac{-31}{12} = \frac{12x^{-31/12}}{9*-31} = \frac{12x^{-31/12}}{-279}$$
This is wrong. The correct answer for this part only would be: $$-\frac{4x^{-31/12}}{31}$$
It seems like I got the exponent correct. But somewhere in doing the reverse power rule I got lost in the sauce. Could someone help? Thanks!