solving limit of sequence by sandwich theorem I am trying to find the limit (as n tends to infinity) of
$$a_n=\left(3^n+9^n\right)^{1/n} $$ and
$$b_n=\left(1+ \frac{7}{8n^3}\right)^{n^3}$$
What I am considering is to use Sandwich Theorem however I dunno how I should start with. Thanks

For the first : $$\begin{align}\lim_{n\to\infty}(3^n+9^n)^{1/n}&=\lim_{n\to\infty}\left(9^n\left(1+\frac{3^n}{9^n}\right)\right)^{1/n}\\&=\lim_{n\to\infty}9\left(1+\frac{1}{3^n}\right)^{1/n}\\&=9\cdot 1\end{align}$$
Here, note that
$$1=1^{1/n}\lt \left(1+\frac{1}{3^n}\right)^{1/n}\lt 1+\frac{1}{3^n}\to 1\ (n\to \infty).$$
For the second : 
$$\lim_{n\to\infty}\left(1+\frac{1}{\frac{8n^3}{7}}\right)^{n^3}=\lim_{n\to\infty}\left(\left(1+\frac{1}{\frac{8n^3}{7}}\right)^{\frac{8n^3}{7}}\right)^{\frac{7}{8}}=e^{7/8}$$
