Distribute the exponent 2 inside the bracket.

Formula: \((a^{b})^{c} = a^{bc}\)

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

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

\(=\sqrt[3]{x^{6}y^{2}y^{4}}\)

Since the bases are for y, so add the exponents.

Formula: \(a^{b}\ \cdot\ a^{c} = a^{b + c}\)

\(=\sqrt[3]{x^{6}y^{2}y^{4}}\)

\(=\sqrt[3]{x^{6}y^{2\ +\ 4}}\)

\(=\sqrt[3]{x^{6}y^{6}}\)

Because of the cube root we have to divide the exponents by 3.

\(\sqrt[3]{x^{6}y^{6}}\)

\(= x^{\frac{6}{3}}y^{\frac{6}{3}}\)

\(= x^{2} y^{2}\)

Finally answer: \(x^{2} y^{2}\)

Formula: \((a^{b})^{c} = a^{bc}\)

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

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

\(=\sqrt[3]{x^{6}y^{2}y^{4}}\)

Since the bases are for y, so add the exponents.

Formula: \(a^{b}\ \cdot\ a^{c} = a^{b + c}\)

\(=\sqrt[3]{x^{6}y^{2}y^{4}}\)

\(=\sqrt[3]{x^{6}y^{2\ +\ 4}}\)

\(=\sqrt[3]{x^{6}y^{6}}\)

Because of the cube root we have to divide the exponents by 3.

\(\sqrt[3]{x^{6}y^{6}}\)

\(= x^{\frac{6}{3}}y^{\frac{6}{3}}\)

\(= x^{2} y^{2}\)

Finally answer: \(x^{2} y^{2}\)