ANSWER
[tex]{2}^{ \frac{1}{6} } [/tex]
EXPLANATION
We want to find the expression that is equivalent to,
[tex] \frac{ \sqrt{2} }{ \sqrt[3]{2} } [/tex]
This is the same as:
[tex] \frac{ {2}^{ \frac{1}{2} } }{ {2}^{ \frac{1}{3} } } [/tex]
Use the following property of indices
[tex] \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} [/tex]
This implies that,
[tex] \frac{ {2}^{ \frac{1}{2} } }{ {2}^{ \frac{1}{3} } } = {2}^{ \frac{1}{2} - \frac{1}{3} } [/tex]
Simplify to obtain,
[tex] {2}^{ \frac{3 - 2}{6} } = {2}^{ \frac{1}{6} } [/tex]
