Solve the Rational Equation for x cube root of 3x=6

$\sqrt[3]{3 x} = 6$

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

${\sqrt[3]{3 x}}^{3} = 6^{3}$

Simplify each side of the equation.

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

${({(3 x)}^{\frac{1}{3}})}^{3} = 6^{3}$

Simplify the left side.

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

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

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

${(3 x)}^{\frac{1}{3} \cdot 3} = 6^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(3 x)}^{\frac{1}{3} \cdot 3} = 6^{3}$

Rewrite the expression.

${(3 x)}^{1} = 6^{3}$

Simplify.

$3 x = 6^{3}$

Simplify the right side.

Raise $6$ to the power of $3$ .

$3 x = 216$

Divide each term in $3 x = 216$ by $3$ and simplify.

Divide each term in $3 x = 216$ by $3$ .

$\frac{3 x}{3} = \frac{216}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{216}{3}$

Divide $x$ by $1$ .

$x = \frac{216}{3}$

Simplify the right side.

Divide $216$ by $3$ .

$x = 72$