Simplify ( cube root of x^2)^2

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

Rewrite ${\sqrt[3]{x^{2}}}^{2}$ as ${({(x^{2})}^{2})}^{\frac{1}{3}}$ .

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

Multiply the exponents in ${(x^{2})}^{2}$ .

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

$\sqrt[3]{x^{2 \cdot 2}}$

Multiply $2$ by $2$ .

$\sqrt[3]{x^{4}}$

Factor out $x^{3}$ .

$\sqrt[3]{x^{3} x}$

Pull terms out from under the radical.

$x \sqrt[3]{x}$