Answer
Proof given below.
Work Step by Step
Let $L=\displaystyle \lim_{n\rightarrow\infty}(x)^{1/n}$, for a positive number $x$
$ L=\displaystyle \lim_{n\rightarrow\infty}(x)^{1/n}\qquad$ ...apply ln(..) to both sides
$\displaystyle \ln L=\ln[\lim_{n\rightarrow\infty}(x)^{1/n}]\qquad$ ... ln is continuous
$\displaystyle \ln L=\lim_{n\rightarrow\infty}[\ln(x)^{1/n}]$
$\displaystyle \ln L=\lim_{n\rightarrow\infty}[\frac{1}{n}\ln x]\qquad$... $\ln x$ is constant when $ n\rightarrow\infty$
$\displaystyle \ln L=\ln x\cdot\lim_{n\rightarrow\infty}[\frac{1}{n}]$
$\ln L=\ln x\cdot 0$
$\ln L=0$
$L=1$
