How do you rationalize the denominator and simplify root3(2/3)?

$\sqrt[3]{\frac{2}{3}} = \frac{\sqrt[3]{18}}{3}$
If $a , b > 0$ then $\sqrt[n]{\frac{a}{b}} = \frac{\sqrt[n]{a}}{\sqrt[n]{b}}$
In our example, rationalize before splitting the cube root by multiplying both numerator and denominator of the radicand by $9$:
$\sqrt[3]{\frac{2}{3}} = \sqrt[3]{\frac{2 \cdot 9}{3 \cdot 9}} = \sqrt[3]{\frac{18}{3} ^ 3} = \frac{\sqrt[3]{18}}{3}$