I tried graphing the functions $y = x^{.42}$ and $y = (x^{42})^{\frac{1}{100}}$. From my understanding of the laws of exponentiation these two expressions should be equivalent. What I found out after graphing these two functions was that they were equivalent for all non negative real numbers. The difference between these two functions was that the domain of $y = (x^{42})^{\frac{1}{100}}$ is $( -\infty, \infty)$ whereas the domain of $y = x^{.42}$ is $[0, \infty)$. I was wondering whether someone could explain why the domain of these two functions is different?