Solve by Factoring cube root of 4x=-2

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

Step 1

Add $2$ to both sides of the equation.

$\sqrt[3]{4 x} + 2 = 0$

Step 2

Subtract $2$ from both sides of the equation.

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

Step 3

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

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

Step 4

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{4 x}$ as ${(4 x)}^{\frac{1}{3}}$ .

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

Simplify the left side.

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

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$4 x = {(- 2)}^{3}$

Simplify the right side.

Raise $- 2$ to the power of $3$ .

$4 x = - 8$

Step 5

Divide each term in $4 x = - 8$ by $4$ and simplify.

Divide each term in $4 x = - 8$ by $4$ .

$\frac{4 x}{4} = \frac{- 8}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 8}{4}$

Divide $x$ by $1$ .

$x = \frac{- 8}{4}$

Simplify the right side.

Divide $- 8$ by $4$ .

$x = - 2$