Simplify (2x^(1/6))^3x^2

${(2 x^{\frac{1}{6}})}^{3} x^{2}$

Apply the product rule to $2 x^{\frac{1}{6}}$ .

$2^{3} {(x^{\frac{1}{6}})}^{3} x^{2}$

Raise $2$ to the power of $3$ .

$8 {(x^{\frac{1}{6}})}^{3} x^{2}$

Multiply the exponents in ${(x^{\frac{1}{6}})}^{3}$ .

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

$8 x^{\frac{1}{6} \cdot 3} x^{2}$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$8 x^{\frac{1}{3 (2)} \cdot 3} x^{2}$

Cancel the common factor.

$8 x^{\frac{1}{3 \cdot 2} \cdot 3} x^{2}$

Rewrite the expression.

$8 x^{\frac{1}{2}} x^{2}$

Multiply $x^{\frac{1}{2}}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$8 (x^{2} x^{\frac{1}{2}})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$8 x^{2 + \frac{1}{2}}$

To write $2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$8 x^{2 \cdot \frac{2}{2} + \frac{1}{2}}$

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

$8 x^{\frac{2 \cdot 2}{2} + \frac{1}{2}}$

Combine the numerators over the common denominator.

$8 x^{\frac{2 \cdot 2 + 1}{2}}$

Simplify the numerator.

Multiply $2$ by $2$ .

$8 x^{\frac{4 + 1}{2}}$

Add $4$ and $1$ .

$8 x^{\frac{5}{2}}$