Arrange the following numbers in increasing order: \begin{align*} A &= \frac{2^{1/2}}{4^{1/6}}\\ B &= \sqrt[12]{128}\vphantom{dfrac{2}{2}}\\ C &= \left( \frac{1}{8^{1/5}} \right)^2\\ D &= \sqrt{\frac{4^{-1}}{2^{-1} \cdot 8^{-1}}}\\ E &= \sqrt[3]{2^{1/2} \cdot 4^{-1/4}}.\vphantom{dfrac{2}{2}} \end{align*}Enter the letters, separated by commas. For example, if you think that $D < A < E < C < B$, then enter "D,A,E,C,B", without the quotation marks.
Note: The following answers are incorrect
C, A, B, E, D
A, C, D, E, B
E, B, D, C, A
