This was a practice problem I was given. 

> 
> Show that $\lim\_{n \rightarrow \infty} \sqrt[n]{a} =1$.
> 
> 
> 

My argument is as follows:
\begin{align}
\lim\_{n \rightarrow \infty} \sqrt[n]{a}
&= \lim\_{n \rightarrow \infty} e^{\ln(\sqrt[n]{a})} \\
&= e^{\lim\_{n \rightarrow \infty}(\frac{1}{n}) \ln(a)} \\
&= e^{\lim\_{n \rightarrow \infty}(0 \cdot \ln(a))} \\
&= e^0 \\
&= 1.\end{align}