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.
+2094 Hint:
We can square root, cube root, etc. or add an exponent to simplify all of the numbers. Then, we can get rid of the fraction easily. Try it out, and if it is still confusing, I will give you another hint!
