Ran into this issue in a class I'm taking.
Say you have a variable $x$.
If you square it and take the square root, you get $\sqrt{x^2}=\pm x$ by the definition of a square root. Taking the square root of something is the same as raising it to the power of $\frac{1}{2}$. So you can also rewrite that expression as $(x^2)^{(1/2)}$.
By the rules of exponents we can rewrite that as $x^{(2 * \frac{1}{2})} = x^1 = x$.
So, somehow, I've gotten the same thing to equal both $\pm x$ and just $x$. What is the missing step in my understanding?
