Solve for x 5-(x-1)^(1/3)=8

$5 - {(x - 1)}^{\frac{1}{3}} = 8$

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

Subtract $5$ from both sides of the equation.

$- {(x - 1)}^{\frac{1}{3}} = 8 - 5$

Subtract $5$ from $8$ .

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

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

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

Simplify the exponent.

Simplify the left side.

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

Apply the product rule to $- {(x - 1)}^{\frac{1}{3}}$ .

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

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

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

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Apply the distributive property.

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

Multiply $- 1$ by $- 1$ .

$- x + 1 = 3^{3}$

Simplify the right side.

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

$- x + 1 = 27$

Solve for $x$ .

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

Subtract $1$ from both sides of the equation.

$- x = 27 - 1$

Subtract $1$ from $27$ .

$- x = 26$

Divide each term in $- x = 26$ by $- 1$ and simplify.

Divide each term in $- x = 26$ by $- 1$ .

$\frac{- x}{- 1} = \frac{26}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{26}{- 1}$

Divide $x$ by $1$ .

$x = \frac{26}{- 1}$

Simplify the right side.

Divide $26$ by $- 1$ .

$x = - 26$

Solve for x 5-(x-1)^(1/3)=8

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