
Finding this derivative
So here's the deal, I already have the answer to a derivative related problem I was doing because I gave up and used an online derivative calculator, which usually (because it shows the steps involved) makes me realize where I was going wrong if I'm having trouble finding a derivative. But this one, even now that I have the answer, confuses me. The original function is t^(1/3)*(216t) and I've gotten as far as (216T/3t^(2/3))T^(1/3) which is correct, since it shows it in the steps on said online derivative calculator.
It then immediately goes from that to simplifying it down to  4(t54)/3t^(2/3)
I understand that 4 factors out of 216 to get the 54, but because there's no 4 in front of the t in the term, and because the t^(1/3) seems to just disappear, I don't understand how the final step of this problem was accomplished. I know the answer is right because I'm doing online homework and it was shown as the correct answer.

Hi
The derivative of $\displaystyle t^{\frac{1}{3}}(216t)$
is $\displaystyle \frac{216t}{3t^{\frac{2}{3}}}t^{\frac{1}{3}}$
Using the same denominator ($\displaystyle {3t^{\frac{2}{3}}}$)
$\displaystyle \frac{216t}{3t^{\frac{2}{3}}}\frac{3t^{\frac{2}{3}}t^{\frac{1}{3}}}{3t^{\frac{2 }{3}}}$
Now $\displaystyle t^{\frac{2}{3}}t^{\frac{1}{3}}=t$
It gives
$\displaystyle \frac{216t}{3t^{\frac{2}{3}}}\frac{3t}{3t^{\frac{2}{3}}}$
$\displaystyle \frac{2164t}{3t^{\frac{2}{3}}}$
$\displaystyle 4\frac{t54}{3t^{\frac{2}{3}}}$

Ahhhh. It's pretty obvious now that I see it, haha. Thanks a bunch