When dividing radicals and the top variable's degree is lower than the bottom's, is it negative? And if so, how does it become written in co

$$\\x^4\div x^6=x^{4-6}=x^{-2}\\\\ $Now I will look at it differently$\\\\ x^4\div x^6=\frac{x^4}{x^6}=\frac{\not{x}\not{x}\not{x}\not{x}^1}{\not{x}\not{x}\not{x}\not{x}xx}=\frac{1}{x^2}\\\\ $so put these together and you get$\\\\ x^{-2}=\frac{1}{x^2}$$

If you want to get rid of a negative indice you put the thing that is raised to the neg power on the other side of the fraction line and change the negative to a positive.  :)

More here:

http://web2.0calc.com/questions/indices-especially-negative-indices