Answer
$\lim\limits_{x \to \infty}x^{1/x}=1$
Work Step by Step
$\lim\limits_{x \to \infty}x^{1/x}=\lim\limits_{x \to \infty}(e^{ln~x})^{1/x}=\lim\limits_{x \to \infty}e^{\frac{1}{x}ln~x}$
$\lim\limits_{x \to \infty}\frac{ln~x}{x} = \lim\limits_{x \to \infty}\frac{(1/x)}{1} = 0$
Therefore:
$\lim\limits_{x \to \infty}e^{\frac{1}{x}ln~x} = e^0 = 1$
