Solve for x fourth root of 3x=12

$\sqrt[4]{3 x} = 12$

To remove the radical on the left side of the equation, raise both sides of the equation to the power of $4$ .

${\sqrt[4]{3 x}}^{4} = 12^{4}$

Simplify each side of the equation.

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

${({(3 x)}^{\frac{1}{4}})}^{4} = 12^{4}$

Simplify the left side.

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

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

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

${(3 x)}^{\frac{1}{4} \cdot 4} = 12^{4}$

Cancel the common factor of $4$ .

Cancel the common factor.

${(3 x)}^{\frac{1}{4} \cdot 4} = 12^{4}$

Rewrite the expression.

${(3 x)}^{1} = 12^{4}$

Simplify.

$3 x = 12^{4}$

Simplify the right side.

Raise $12$ to the power of $4$ .

$3 x = 20736$

Divide each term in $3 x = 20736$ by $3$ and simplify.

Divide each term in $3 x = 20736$ by $3$ .

$\frac{3 x}{3} = \frac{20736}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{20736}{3}$

Divide $x$ by $1$ .

$x = \frac{20736}{3}$

Simplify the right side.

Divide $20736$ by $3$ .

$x = 6912$