The first three terms of a geometric progression are $\sqrt{2}, \sqrt[3]{2}, \sqrt[6]{2}$. Find the fourth term.
$\textbf{(A)}\ 1\qquad \textbf{(B)}\ \sqrt[7]{2}\qquad \textbf{(C)}\ \sqrt[8]{2}\qquad \textbf{(D)}\ \sqrt[9]{2}\qquad \textbf{(E)}\ \sqrt[10]{2}$
After rewriting the radicals as fractional exponents, the sequence is $2^{1/2}, 2^{1/3}, 2^{1/6}$.
The common ratio of the [geometric sequence](https://artofproblemsolving.com/wiki/index.php/Geometric_sequence) is $\frac{2^{1/3}}{2^{1/2}} = 2^{-1/6}$.  Multiplying that by the third term results in $2^0$.  It simplifies to $1$, so the answer is $\boxed{\textbf{(A)}}$.