Solve for x (4-x)^(1/3)-2=3

${(4 - x)}^{\frac{1}{3}} - 2 = 3$

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

Add $2$ to both sides of the equation.

${(4 - x)}^{\frac{1}{3}} = 3 + 2$

Add $3$ and $2$ .

${(4 - x)}^{\frac{1}{3}} = 5$

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

${({(4 - x)}^{\frac{1}{3}})}^{3} = 5^{3}$

Simplify the exponent.

Simplify the left side.

Simplify ${({(4 - x)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(4 - x)}^{\frac{1}{3}})}^{3}$ .

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

${(4 - x)}^{\frac{1}{3} \cdot 3} = 5^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(4 - x)}^{\frac{1}{3} \cdot 3} = 5^{3}$

Rewrite the expression.

${(4 - x)}^{1} = 5^{3}$

Simplify.

$4 - x = 5^{3}$

Simplify the right side.

Raise $5$ to the power of $3$ .

$4 - x = 125$

Solve for $x$ .

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

Subtract $4$ from both sides of the equation.

$- x = 125 - 4$

Subtract $4$ from $125$ .

$- x = 121$

Divide each term in $- x = 121$ by $- 1$ and simplify.

Divide each term in $- x = 121$ by $- 1$ .

$\frac{- x}{- 1} = \frac{121}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{121}{- 1}$

Divide $x$ by $1$ .

$x = \frac{121}{- 1}$

Simplify the right side.

Divide $121$ by $- 1$ .

$x = - 121$