Solve for y x=1/3( fourth root of y)

$x = \frac{1}{3} (\sqrt[4]{y})$

Step 1

Rewrite the equation as $\frac{1}{3} \cdot \sqrt[4]{y} = x$ .

$\frac{1}{3} \cdot \sqrt[4]{y} = x$

Step 2

Multiply both sides of the equation by $3$ .

$3 (\frac{1}{3} \cdot \sqrt[4]{y}) = 3 x$

Step 3

Simplify the left side.

Simplify $3 (\frac{1}{3} \cdot \sqrt[4]{y})$ .

Combine $\frac{1}{3}$ and $\sqrt[4]{y}$ .

$3 \frac{\sqrt[4]{y}}{3} = 3 x$

Cancel the common factor of $3$ .

Cancel the common factor.

$3 \frac{\sqrt[4]{y}}{3} = 3 x$

Rewrite the expression.

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

Step 4

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

${\sqrt[4]{y}}^{4} = {(3 x)}^{4}$

Step 5

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$y = {(3 x)}^{4}$

Simplify the right side.

Simplify ${(3 x)}^{4}$ .

Apply the product rule to $3 x$ .

$y = 3^{4} x^{4}$

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

$y = 81 x^{4}$