Getting the root out of the denominator Alright quick question, 
If I have 
$$\frac{1}{2^{1/3} - 2},$$
how do i change it to not have the root in the denominator? I know the trick with the root of 2, but this seems a bit more complicated. Thanks in advance :)

If you mean
$$\frac{1}{2^{1/3}} - 2,$$
then just multiply the numerator and denominator by $2^{2/3}$; we get
$$\frac{2^{2/3}}{2} - 2.$$
If you mean
$$\frac{1}{2^{1/3} - 2}$$
then you can use the formula
$$(a-b)(a^2+ab+b^2) = a^3-b^3$$
so
$$\frac{1}{2^{1/3}-2} = \frac{2^{2/3} + 2(2^{1/3}) + 4}{(2^{1/3}-2)(2^{2/3} + 2(2^{1/3})+4)} = \frac{2^{2/3} + 2^{4/3} + 4}{2 - 8} = -\frac{2^{2/3} + 2^{4/3} + 4}{6}. $$
