Solve for x (3x)^(1/3)=-3

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

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

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

Simplify the exponent.

Simplify the left side.

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

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

${(3 x)}^{1} = {(- 3)}^{3}$

Simplify.

$3 x = {(- 3)}^{3}$

Simplify the right side.

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

$3 x = - 27$

Divide each term in $3 x = - 27$ by $3$ and simplify.

Divide each term in $3 x = - 27$ by $3$ .

$\frac{3 x}{3} = \frac{- 27}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 27}{3}$

Divide $x$ by $1$ .

$x = \frac{- 27}{3}$

Simplify the right side.

Divide $- 27$ by $3$ .

$x = - 9$