Solve for x y=2x^(1/3)

$y = 2 x^{\frac{1}{3}}$

Rewrite the equation as $2 x^{\frac{1}{3}} = y$ .

$2 x^{\frac{1}{3}} = y$

Divide each term in $2 x^{\frac{1}{3}} = y$ by $2$ and simplify.

Divide each term in $2 x^{\frac{1}{3}} = y$ by $2$ .

$\frac{2 x^{\frac{1}{3}}}{2} = \frac{y}{2}$

Simplify the left side.

Cancel the common factor.

$\frac{2 x^{\frac{1}{3}}}{2} = \frac{y}{2}$

Divide $x^{\frac{1}{3}}$ by $1$ .

$x^{\frac{1}{3}} = \frac{y}{2}$

Raise each side of the equation to the power of $3$ to eliminate the fractional exponent on the left side.

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

Simplify the exponent.

Simplify the left side.

Simplify ${(x^{\frac{1}{3}})}^{3}$ .

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Simplify the right side.

Simplify ${(\frac{y}{2})}^{3}$ .

Apply the product rule to $\frac{y}{2}$ .

$x = \frac{y^{3}}{2^{3}}$

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

$x = \frac{y^{3}}{8}$