Solve by Factoring cube root of x-5=-6

$\sqrt[3]{x - 5} = - 6$

Step 1

Add $6$ to both sides of the equation.

$\sqrt[3]{x - 5} + 6 = 0$

Step 2

Subtract $6$ from both sides of the equation.

$\sqrt[3]{x - 5} = - 6$

Step 3

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

${\sqrt[3]{x - 5}}^{3} = {(- 6)}^{3}$

Step 4

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x - 5}$ as ${(x - 5)}^{\frac{1}{3}}$ .

${({(x - 5)}^{\frac{1}{3}})}^{3} = {(- 6)}^{3}$

Simplify the left side.

Simplify ${({(x - 5)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(x - 5)}^{\frac{1}{3}})}^{3}$ .

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

${(x - 5)}^{\frac{1}{3} \cdot 3} = {(- 6)}^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(x - 5)}^{\frac{1}{3} \cdot 3} = {(- 6)}^{3}$

Rewrite the expression.

${(x - 5)}^{1} = {(- 6)}^{3}$

Simplify.

$x - 5 = {(- 6)}^{3}$

Simplify the right side.

Raise $- 6$ to the power of $3$ .

$x - 5 = - 216$

Step 5

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

Add $5$ to both sides of the equation.

$x = - 216 + 5$

Add $- 216$ and $5$ .

$x = - 211$