# Simplify radicals and exponents sqrt[3]{(x^{3} y)^{2}y^{4}}

Question
Simplify radicals and exponents $$\sqrt[3]{(x^{3}\ y)^{2}y^{4}}$$

2021-03-02
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: $$x^{2} y^{2}$$

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