Could someone explain how/why the square root of $x$ equals $x$ to the one half power? I know by definition it does, but is there any mathematical process we can go through to get from one to the other?  In addition, I know the $x$ to the 2ed power is equal to $x*x$, but what is $x^{1/2}$ equal to? Is it one half of $x$ times one half of $x$? No!  I know all this stuff by definition, but I want to know why. Thanks
Why is ${x^{\frac{1}{2}}}$ the same as $\sqrt x $?   I'm currently studying indices/exponents, and this is a law that I was told to accept without much proof or explanation, could someone explain the reasoning behind this.  Thank you.
I am trying to help my daughter on her math homework and I am having some trouble on some equation solving steps. My current major concern relies on understanding why $\sqrt{8}/2$ equal to $\sqrt{2}$.  Thanks in advance