Arrange the following numbers in increasing order:

Here is the increasing order:
C = 0.43527528164,  E = 1,    A=1.122462048,    B=1.498307077,    D = 2

$$\begin{align*} A &= \frac{2^{1/2}}{4^{1/6}}\\ B &= \sqrt[12]{128}\vphantom{dfrac{2}{2}}\\ C &= \left( \frac{1}{8^{1/5}} \right)^2\\ D &= \sqrt{\frac{4^{-1}}{2^{-1} \cdot 8^{-1}}}\\ E &= \sqrt[3]{2^{1/2} \cdot 4^{-1/4}}\vphantom{dfrac{2}{2}} \end{align*}$$

$\begin{align*} A &= \frac{2^{1/2}}{4^{1/6}}=2^{0.5-0.\dot3}=2^{1/6}=2^{2/12}\\ B &= \sqrt[12]{128}\vphantom{dfrac{2}{2}}=\sqrt[12]{2^7}\vphantom{dfrac{2}{2}}=2^{7/12} \end{align*} etc$

Change them all to powers of 2.

And stop accusing other people of cheating (on other threads)

It is irritating.