Evaluate ( cube root of x^2)^6

${(\sqrt[3]{x^{2}})}^{6}$

Step 1

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

${(x^{\frac{2}{3}})}^{6}$

Step 2

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

$x^{\frac{2}{3} \cdot 6}$

Step 3

Combine $\frac{2}{3}$ and $6$ .

$x^{\frac{2 \cdot 6}{3}}$

Step 4

Multiply $2$ by $6$ .

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

Step 5

Cancel the common factor of $12$ and $3$ .

Factor $3$ out of $12$ .

$x^{\frac{3 \cdot 4}{3}}$

Cancel the common factors.

Factor $3$ out of $3$ .

$x^{\frac{3 \cdot 4}{3 (1)}}$

Cancel the common factor.

$x^{\frac{3 \cdot 4}{3 \cdot 1}}$

Rewrite the expression.

$x^{\frac{4}{1}}$

Divide $4$ by $1$ .

$x^{4}$