Simplify ( cube root of x^3y^2)^12

${(\sqrt[3]{x^{3} y^{2}})}^{12}$

Pull terms out from under the radical.

${(x \sqrt[3]{y^{2}})}^{12}$

Apply the product rule to $x \sqrt[3]{y^{2}}$ .

$x^{12} {\sqrt[3]{y^{2}}}^{12}$

Rewrite ${\sqrt[3]{y^{2}}}^{12}$ as $y^{8}$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{y^{2}}$ as $y^{\frac{2}{3}}$ .

$x^{12} {(y^{\frac{2}{3}})}^{12}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{12} y^{\frac{2}{3} \cdot 12}$

Combine $\frac{2}{3}$ and $12$ .

$x^{12} y^{\frac{2 \cdot 12}{3}}$

Multiply $2$ by $12$ .

$x^{12} y^{\frac{24}{3}}$

Cancel the common factor of $24$ and $3$ .

Factor $3$ out of $24$ .

$x^{12} y^{\frac{3 \cdot 8}{3}}$

Cancel the common factors.

Factor $3$ out of $3$ .

$x^{12} y^{\frac{3 \cdot 8}{3 (1)}}$

Cancel the common factor.

$x^{12} y^{\frac{3 \cdot 8}{3 \cdot 1}}$

Rewrite the expression.

$x^{12} y^{\frac{8}{1}}$

Divide $8$ by $1$ .

$x^{12} y^{8}$