Sorry im redoing it accidently submitted the wrong thing
Here was my attempt it was actuly a derivative problem but i decided not to post in the calculus section.
$\displaystyle \frac {1}{3} (1-e^{6x})^{\frac{-2}{3}} * (- e^{6x} * 6)$
$\displaystyle = (2 - 2e^{6x}) ^{\frac{-2}{3}} * -e^{6x}$
$\displaystyle = \frac{1}{(2-2e^{6x})^{\frac{2}{3}}} - e^{6x}$
You can't distribute the two to the binomial expression because that expression is an infinite sum and the 2 is not raised to the same power.
$\displaystyle \frac{1}{3}(1-e^{6x})^{2/3} \cdot -6e^{6x}$
$\displaystyle = 2e^{6x}(1-e^{6x})^{2/3}$
You cannot simplify that further.
EDIT: If you're planning on finding the derivative use the product rule and the chain rule
I'm assuming you are taking the derivative of f(x):
$\displaystyle f(x) = (1 - e^{6x})^{\frac{1}{3}}$
In that case, you made errors in both the second and third steps.
(second step) You can't put the multiple of 2 inside the $\displaystyle (1 - e^{6x})^{-\frac{2}{3}}$ term.
(third step) You should be multiplying by $\displaystyle -e^{6x}$, not subtracting $\displaystyle e^{6x}$.