Solve for m -4 = cube root of m+2

$- 4 = \sqrt[3]{m + 2}$

Rewrite the equation as $\sqrt[3]{m + 2} = - 4$ .

$\sqrt[3]{m + 2} = - 4$

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

${\sqrt[3]{m + 2}}^{3} = {(- 4)}^{3}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{m + 2}$ as ${(m + 2)}^{\frac{1}{3}}$ .

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

Simplify the left side.

Simplify ${({(m + 2)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(m + 2)}^{\frac{1}{3}})}^{3}$ .

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

${(m + 2)}^{1} = {(- 4)}^{3}$

Simplify.

$m + 2 = {(- 4)}^{3}$

Simplify the right side.

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

$m + 2 = - 64$

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

Subtract $2$ from both sides of the equation.

$m = - 64 - 2$

Subtract $2$ from $- 64$ .

$m = - 66$