The rule for rewriting rational exponents is: $\displaystyle{{x}}^{{\frac{{m}}{{n}}}}={\sqrt[{{n}}]{{{{x}}^{{m}}}}}\usepackage{cmbright}\Huge\$

The denominator of the fraction is 3, so the radical will be for a third root. Because there are parentheses, the exponent refers to the quantity within the parentheses.

$\displaystyle{{\left({2}{y}\right)}}^{{\frac{{2}}{{3}}}}={\sqrt[{{3}}]{{{{\left({2}{y}\right)}}^{{2}}}}}\usepackage{cmbright}\Huge\$