Solve by Factoring (x+4)^(1/3)-2=-6

${(x + 4)}^{\frac{1}{3}} - 2 = - 6$

Step 1

Add $6$ to both sides of the equation.

${(x + 4)}^{\frac{1}{3}} - 2 + 6 = 0$

Step 2

Add $- 2$ and $6$ .

${(x + 4)}^{\frac{1}{3}} + 4 = 0$

Step 3

Subtract $4$ from both sides of the equation.

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

Step 4

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

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

Step 5

Simplify the exponent.

Simplify the left side.

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

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$x + 4 = {(- 4)}^{3}$

Simplify the right side.

Raise $- 4$ to the power of $3$ .

$x + 4 = - 64$

Step 6

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

Subtract $4$ from both sides of the equation.

$x = - 64 - 4$

Subtract $4$ from $- 64$ .

$x = - 68$