express (2y)^2/3 in radical form

Answer 1

To express \((2y)^{\frac{2}{3}}\) in radical form, you can separate the fraction into two parts: the numerator and the denominator.

1. The numerator is \(2^2y^2\), which equals \(4y^2\).
2. The denominator is \(3\), which indicates that we will take the cube root.

Thus, you can write it as:

\[ (2y)^{\frac{2}{3}} = \sqrt[3]{(2y)^2} = \sqrt[3]{4y^2} \]

So, the expression \((2y)^{\frac{2}{3}}\) in radical form is:

\[ \sqrt[3]{4y^2} \]