Solve for x 3x^(1/3)-2=-4

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

Step 1

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

Add $2$ to both sides of the equation.

$3 x^{\frac{1}{3}} + 4 = 2$

Subtract $4$ from both sides of the equation.

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

Subtract $4$ from $2$ .

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

Step 2

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

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

Step 3

Simplify the exponent.

Simplify the left side.

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

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

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

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

$27 {(x^{\frac{1}{3}})}^{3} = {(- 2)}^{3}$

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

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

$27 x^{\frac{1}{3} \cdot 3} = {(- 2)}^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$27 x^{\frac{1}{3} \cdot 3} = {(- 2)}^{3}$

Rewrite the expression.

$27 x^{1} = {(- 2)}^{3}$

Simplify.

$27 x = {(- 2)}^{3}$

Simplify the right side.

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

$27 x = - 8$

Step 4

Divide each term in $27 x = - 8$ by $27$ and simplify.

Divide each term in $27 x = - 8$ by $27$ .

$\frac{27 x}{27} = \frac{- 8}{27}$

Simplify the left side.

Cancel the common factor of $27$ .

Cancel the common factor.

$\frac{27 x}{27} = \frac{- 8}{27}$

Divide $x$ by $1$ .

$x = \frac{- 8}{27}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{8}{27}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{8}{27}$

Decimal Form:

$x = - 0.\overline{296}$

Solve for x 3x^(1/3)-2=-4

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