Solve the Rational Equation for x 3 cube root of x=12

$3 \sqrt[3]{x} = 12$

Step 1

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

${(3 \sqrt[3]{x})}^{3} = 12^{3}$

Step 2

Simplify each side of the equation.

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

${(3 x^{\frac{1}{3}})}^{3} = 12^{3}$

Simplify the left side.

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

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

$3^{3} {(x^{\frac{1}{3}})}^{3} = 12^{3}$

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

$27 {(x^{\frac{1}{3}})}^{3} = 12^{3}$

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

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

$27 x^{\frac{1}{3} \cdot 3} = 12^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$27 x^{\frac{1}{3} \cdot 3} = 12^{3}$

Rewrite the expression.

$27 x^{1} = 12^{3}$

Simplify.

$27 x = 12^{3}$

Simplify the right side.

Raise $12$ to the power of $3$ .

$27 x = 1728$

Step 3

Divide each term in $27 x = 1728$ by $27$ and simplify.

Divide each term in $27 x = 1728$ by $27$ .

$\frac{27 x}{27} = \frac{1728}{27}$

Simplify the left side.

Cancel the common factor of $27$ .

Cancel the common factor.

$\frac{27 x}{27} = \frac{1728}{27}$

Divide $x$ by $1$ .

$x = \frac{1728}{27}$

Simplify the right side.

Divide $1728$ by $27$ .

$x = 64$