Find the value of $3^9\cdot 3^3\cdot 3\cdot 3^{1/3}\cdot\cdots$ 
Find the value of $3^9\cdot 3^3\cdot 3\cdot 3^{1/3}\cdot\cdots$

Doesn't this thing approaches 0 at the end?  why does it approaches 1?

HINT:
Using Exponent Combination Laws,
$$a^m\cdot a^n\cdot a^p\cdots=a^{m+n+p+\cdot},$$
$$\displaystyle 3^9\cdot 3^3\cdot3\cdot 3^\frac13\cdots=3^{\left(3^2+3+1+\frac13+\cdots\right)}$$
Observe that the power of $3$ is an infinite Geometric Series with the first Term $=9$ and common ratio $=\frac13<1$
