The given expression is [tex] \frac{\sqrt{2}}{\sqrt[3]{2}} [/tex]
This can be simplified using the radical properties as below
[tex] \\\ \frac{\sqrt{2}}{\sqrt[3]{2}}=\frac{2^{\frac{1}{2}}}{2^\frac{1}{3}} \\\\ \frac{\sqrt{2}}{\sqrt[3]{2}}=\frac{2^{\frac{1}{2}}}{2^\frac{1}{3}} \\\\ [/tex]
Now using exponent properties we can write
[tex] \\\ \frac{\sqrt{2}}{\sqrt[3]{2}}=\frac{2^{\frac{1}{2}}}{2^\frac{1}{3}}=2^{\frac{1}{2}-\frac{1}{3}} \\\\\frac{\sqrt{2}}{\sqrt[3]{2}}=2^{\frac{3-2}{6}}=2^\frac{1}{6}\\\\= \sqrt[6]{2}\\ [/tex]
