Answer:
[tex]\frac{2}{3}^{\frac{1}{3}}[/tex]
Step-by-step explanation:
The n-th root is the same thing as the denominator of an exponent.
For example. [tex]\sqrt[3]{x} = x^{\frac{1}{3}}[/tex]
and [tex]\sqrt[4]{x} = x^{\frac{1}{4}}[/tex]
and [tex]\sqrt{x} = x^{\frac{1}{2}}[/tex]
So
[tex]\sqrt[6]{\frac{2}{3}^{2}} = \frac{2}{3}^{(2)(\frac{1}{6})} = \frac{2}{3}^{\frac{2}{6}} = \frac{2}{3}^{\frac{1}{3}}[/tex]
