To determine which of the given expressions is equivalent to [tex]\(\frac{\sqrt[4]{6}}{\sqrt[3]{2}}\)[/tex] (denoted as [tex]\(A\)[/tex]), let's rewrite each expression in terms of roots and see if they match the form of [tex]\(A\)[/tex].
Given:
[tex]\[ A = \frac{\sqrt[4]{6}}{\sqrt[3]{2}} \][/tex]
Let's go through each of the given expressions one by one:
1. [tex]\(\frac{\sqrt[12]{27}}{2}\)[/tex]
2. [tex]\(\frac{\sqrt[4]{24}}{2}\)[/tex]
3. [tex]\(\frac{\sqrt[12]{55296}}{2}\)[/tex]
4. [tex]\(\frac{\sqrt[12]{177147}}{3}\)[/tex]
After evaluating each expression and comparing it to [tex]\(\frac{\sqrt[4]{6}}{\sqrt[3]{2}}\)[/tex], none of the given expressions match the value of [tex]\( \frac{\sqrt[4]{6}}{\sqrt[3]{2}} \)[/tex].
Therefore, the answer is:
[tex]\[
\boxed{\text{None of the above}}
\][/tex]
