SOLUTION —
$2^{1 / 4} \cdot 4^{1 / 8} \cdot 8^{1 / 16} \cdot 16^{1 / 32} \cdot \ldots \infty$
$=2^{\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\ldots}$
$=2^{\frac{1}{4}\left(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\cdots\right)} $
$=2^{\frac{1}{4}\left(\frac{1}{1-\frac{1}{2}}\right)}=\sqrt{2}$
So, The correct option will be (B).