Algebra Examples

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

Step 1

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

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

Step 2

Divide each term in $3 \sqrt[4]{x} = y$ by $3$ and simplify.

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Step 2.1

Divide each term in $3 \sqrt[4]{x} = y$ by $3$ .

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $3$ .

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Step 2.2.1.1

Cancel the common factor.

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

Step 2.2.1.2

Divide $\sqrt[4]{x}$ by $1$ .

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

Step 3

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

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

Step 4

Simplify each side of the equation.

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Step 4.1

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

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

Step 4.2

Simplify the left side.

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Step 4.2.1

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

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Step 4.2.1.1

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

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Step 4.2.1.1.1

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

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

Step 4.2.1.1.2

Cancel the common factor of $4$ .

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Step 4.2.1.1.2.1

Cancel the common factor.

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

Step 4.2.1.1.2.2

Rewrite the expression.

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

Step 4.2.1.2

Simplify.

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

Step 4.3

Simplify the right side.

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Step 4.3.1

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

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Step 4.3.1.1

Apply the product rule to $\frac{y}{3}$ .

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

Step 4.3.1.2

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

$x = \frac{y^{4}}{81}$