Solve for x cube root of x/3=-2

$\sqrt[3]{\frac{x}{3}} = - 2$

To remove the radical on the left side of the equation, cube both sides of the equation.

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

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{\frac{x}{3}}$ as ${(\frac{x}{3})}^{\frac{1}{3}}$ .

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

Simplify the left side.

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

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Simplify the right side.

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

$\frac{x}{3} = - 8$

Solve for $x$ .

Multiply both sides of the equation by $3$ .

$3 \frac{x}{3} = 3 \cdot - 8$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$3 \frac{x}{3} = 3 \cdot - 8$

Rewrite the expression.

$x = 3 \cdot - 8$

Simplify the right side.

Multiply $3$ by $- 8$ .

$x = - 24$