Solving $x^{2n} = \frac{1}{2^n}$ for $x$ What is the principle behind solving for a variable that is raised to another variable?  I came across this problem doing infinite sums: I had to solve the equation 
$$x^{2n} = \frac{1}{2^n}$$
for $x$. I posed the question in the online forum and the TA said the answer is 
$$x = \frac{1}{\sqrt{2}}.$$  
I don't see how he got there.  If someone could explain how to get from one to the other, I would appreciate it!

$x^{2n}=(x^2)^n=\frac{1}{2^n}$. So if $n\neq 0$, for $x\in \mathbb{R}$ you have $x^2=\frac{1}{2}$ then $x=\frac{1}{\sqrt{2}}$ or $x=-\frac{1}{\sqrt{2}}$.
