How does an exponent work when it's less than one? I'm rather familiar with exponents, I know that $y^x = y_1 \cdot y_2 \cdot y_3 .... y_x$, but what if the exponent is less than one, how would that work? 
I put in my computer $25^{1/2}$ anyway, expecting it to give me an error, and I got an answer!! And even more surprising, when I did this with more numbers and a little research, I found that $$x^{1/y} = \sqrt[y] x$$ Is it just me, or can exponents take on the role of square roots?

$$y^x = y\cdots y$$
only if $x$ is a positive integer.
In general:
$$y^x = \exp(x\log y)$$
provided that $y >0$ (the functions $\exp$ and $\log$ can be defined via power series).
Also one can prove:
$$\sqrt[x]{y} = y^{1/x}$$
as you noted (this can also be taken as the definition of roots).
