Solve for x cube root of 1-x=-1

$\sqrt[3]{1 - x} = - 1$

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

${\sqrt[3]{1 - x}}^{3} = {(- 1)}^{3}$

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Simplify the right side.

Raise $- 1$ to the power of $3$ .

$1 - x = - 1$

Solve for $x$ .

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

Subtract $1$ from both sides of the equation.

$- x = - 1 - 1$

Subtract $1$ from $- 1$ .

$- x = - 2$

Divide each term in $- x = - 2$ by $- 1$ and simplify.

Divide each term in $- x = - 2$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 2}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 2}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 2}{- 1}$

Simplify the right side.

Divide $- 2$ by $- 1$ .

$x = 2$