General Math Questions, exponents

Hey, I'm working on my math homework and I've come across several questions that I was hoping someone could please clarify for me.

1. After simplifying the addition I came up with an answer that has x^7 + x^6 + x^5 etc....(with coefficients in front as well, just simplified it for post) all divided by (1- 2x^4) --> is this fully simplified? I would like to factor it further but the only way I know how to simplify it further is through the long trial and error method of finding one factor than using long division.

2. I have a question that has cuberoot (x + 1) * 3(cuberoot (x+1)^2)

Am I allowed to just multiply it through so that I get (x+1)^3 and then cancel the three with the cuberoot or is there some other method that I am supposed to use.

3. (similar to my first question) --> the question asks to simplify and after doing a couple things I'm stuck at:

(10x^7 - 5 + 15x^3 + 20x^5)/ x^4

I don't think this is fully simplified but I'm unsure of how to combine or factor these piece parts.

The original question was:

10x^3 - 5x^(-4) + 15x^(-1) + 20x

4. Am I allowed to split up division: for example: (2/5 + 2/4)/5 = (2/5)/5 + (2/4)/5 ??? (In the cases i tried it worked but I figured I would ask the question anyways)

Sorry for long post (I keep adding as I go) Please help!!!!!

thanks, bye