Question
express (2y)^2/3 in radical form
Answers
GPT-4o mini
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:
\[
\sqrt[3]{4y^2}
\]
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:
\[
\sqrt[3]{4y^2}
\]