Solve the Rational Equation for x cube root of 2x=4

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

Step 1

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

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

Step 2

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$2 x = 4^{3}$

Simplify the right side.

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

$2 x = 64$

Step 3

Divide each term in $2 x = 64$ by $2$ and simplify.

Divide each term in $2 x = 64$ by $2$ .

$\frac{2 x}{2} = \frac{64}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{64}{2}$

Divide $x$ by $1$ .

$x = \frac{64}{2}$

Simplify the right side.

Divide $64$ by $2$ .

$x = 32$