Solve for x (9-x)^(1/3)+12=15

${(9 - x)}^{\frac{1}{3}} + 12 = 15$

Move all terms not containing $x$ to the right side of the equation.

Subtract $12$ from both sides of the equation.

${(9 - x)}^{\frac{1}{3}} = 15 - 12$

Subtract $12$ from $15$ .

${(9 - x)}^{\frac{1}{3}} = 3$

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

${({(9 - x)}^{\frac{1}{3}})}^{3} = 3^{3}$

Simplify the exponent.

Simplify the left side.

Simplify ${({(9 - x)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(9 - x)}^{\frac{1}{3}})}^{3}$ .

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

${(9 - x)}^{\frac{1}{3} \cdot 3} = 3^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(9 - x)}^{\frac{1}{3} \cdot 3} = 3^{3}$

Rewrite the expression.

${(9 - x)}^{1} = 3^{3}$

Simplify.

$9 - x = 3^{3}$

Simplify the right side.

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

$9 - x = 27$

Solve for $x$ .

Move all terms not containing $x$ to the right side of the equation.

Subtract $9$ from both sides of the equation.

$- x = 27 - 9$

Subtract $9$ from $27$ .

$- x = 18$

Divide each term in $- x = 18$ by $- 1$ and simplify.

Divide each term in $- x = 18$ by $- 1$ .

$\frac{- x}{- 1} = \frac{18}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{18}{- 1}$

Divide $x$ by $1$ .

$x = \frac{18}{- 1}$

Simplify the right side.

Divide $18$ by $- 1$ .

$x = - 18$