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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.

 May 26, 2021
 #1
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Write everything in terms of powers of $2$. Then use that $2^n<2^N$ if and only if $n

 May 26, 2021
edited by thedudemanguyperson  May 26, 2021

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