Algebra Examples

$\frac{2}{\sqrt[4]{4 y}}$

Step 1

Multiply $\frac{2}{\sqrt[4]{4 y}}$ by $\frac{{\sqrt[4]{4 y}}^{3}}{{\sqrt[4]{4 y}}^{3}}$ .

$\frac{2}{\sqrt[4]{4 y}} \cdot \frac{{\sqrt[4]{4 y}}^{3}}{{\sqrt[4]{4 y}}^{3}}$

Step 2

Simplify terms.

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Step 2.1

Combine and simplify the denominator.

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Step 2.1.1

Multiply $\frac{2}{\sqrt[4]{4 y}}$ by $\frac{{\sqrt[4]{4 y}}^{3}}{{\sqrt[4]{4 y}}^{3}}$ .

$\frac{2 {\sqrt[4]{4 y}}^{3}}{\sqrt[4]{4 y} {\sqrt[4]{4 y}}^{3}}$

Step 2.1.2

Raise $\sqrt[4]{4 y}$ to the power of $1$ .

$\frac{2 {\sqrt[4]{4 y}}^{3}}{{\sqrt[4]{4 y}}^{1} {\sqrt[4]{4 y}}^{3}}$

Step 2.1.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{2 {\sqrt[4]{4 y}}^{3}}{{\sqrt[4]{4 y}}^{1 + 3}}$

Step 2.1.4

Add $1$ and $3$ .

$\frac{2 {\sqrt[4]{4 y}}^{3}}{{\sqrt[4]{4 y}}^{4}}$

Step 2.1.5

Rewrite ${\sqrt[4]{4 y}}^{4}$ as $4 y$ .

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Step 2.1.5.1

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

$\frac{2 {\sqrt[4]{4 y}}^{3}}{{({(4 y)}^{\frac{1}{4}})}^{4}}$

Step 2.1.5.2

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

$\frac{2 {\sqrt[4]{4 y}}^{3}}{{(4 y)}^{\frac{1}{4} \cdot 4}}$

Step 2.1.5.3

Combine $\frac{1}{4}$ and $4$ .

$\frac{2 {\sqrt[4]{4 y}}^{3}}{{(4 y)}^{\frac{4}{4}}}$

Step 2.1.5.4

Cancel the common factor of $4$ .

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Step 2.1.5.4.1

Cancel the common factor.

$\frac{2 {\sqrt[4]{4 y}}^{3}}{{(4 y)}^{\frac{4}{4}}}$

Step 2.1.5.4.2

Rewrite the expression.

$\frac{2 {\sqrt[4]{4 y}}^{3}}{{(4 y)}^{1}}$

Step 2.1.5.5

Simplify.

$\frac{2 {\sqrt[4]{4 y}}^{3}}{4 y}$

Step 2.2

Cancel the common factor of $2$ and $4$ .

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Step 2.2.1

Factor $2$ out of $2 {\sqrt[4]{4 y}}^{3}$ .

$\frac{2 ({\sqrt[4]{4 y}}^{3})}{4 y}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $2$ out of $4 y$ .

$\frac{2 ({\sqrt[4]{4 y}}^{3})}{2 (2 y)}$

Step 2.2.2.2

Cancel the common factor.

$\frac{2 {\sqrt[4]{4 y}}^{3}}{2 (2 y)}$

Step 2.2.2.3

Rewrite the expression.

$\frac{{\sqrt[4]{4 y}}^{3}}{2 y}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite ${\sqrt[4]{4 y}}^{3}$ as $\sqrt[4]{{(4 y)}^{3}}$ .

$\frac{\sqrt[4]{{(4 y)}^{3}}}{2 y}$

Step 3.2

Apply the product rule to $4 y$ .

$\frac{\sqrt[4]{4^{3} y^{3}}}{2 y}$

Step 3.3

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

$\frac{\sqrt[4]{64 y^{3}}}{2 y}$

Step 3.4

Rewrite $64 y^{3}$ as $2^{4} \cdot (4 y^{3})$ .

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Step 3.4.1

Factor $16$ out of $64$ .

$\frac{\sqrt[4]{16 (4) y^{3}}}{2 y}$

Step 3.4.2

Rewrite $16$ as $2^{4}$ .

$\frac{\sqrt[4]{2^{4} \cdot 4 y^{3}}}{2 y}$

Step 3.4.3

Add parentheses.

$\frac{\sqrt[4]{2^{4} \cdot (4 y^{3})}}{2 y}$

Step 3.5

Pull terms out from under the radical.

$\frac{2 \sqrt[4]{4 y^{3}}}{2 y}$

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Cancel the common factor.

$\frac{2 \sqrt[4]{4 y^{3}}}{2 y}$

Step 4.2

Rewrite the expression.

$\frac{\sqrt[4]{4 y^{3}}}{y}$