Which expression is equivalent to [tex]\frac{\sqrt[4]{6}}{\sqrt[3]{2}}[/tex]?

A. [tex]\frac{\sqrt[12]{27}}{2}[/tex]
B. [tex]\frac{\sqrt[4]{24}}{2}[/tex]
C. [tex]\frac{\sqrt[12]{55296}}{2}[/tex]
D. [tex]\frac{\sqrt[12]{177147}}{3}[/tex]



Answer :

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]