Answer: The answer is [tex]x^2y^2\sqrt[3]{y^2}.[/tex]
Step-by-step explanation: The given expression is as follows
[tex](x^3y^4)^{\frac{2}{3}}.[/tex]
We are given to convert the above expression to the simplest radical form. For that, first we need to evaluate the n-th roots, then we need to evaluate the integral powers, and then we can reach at our desired result.
The conversion is as follows -
[tex](x^3y^4)^{\frac{2}{3}}\\\\=\sqrt[3]{(x^3y^4)^2}\\\\ =\sqrt[3]{x^6y^8}\\\\=x^{\frac{6}{3}}y^{\frac{8}{3}}\\\\=x^2y^{2+\frac{2}{3}}\\\\=x^2y^2y^\frac{2}{3}\\\\=x^2y^2\sqrt[3]{y^2}.[/tex]
Thus, the answer is
[tex]x^2y^2\sqrt[3]{y^2}.[/tex]
