Simplify the Radical Expression (8y^2)/(2 fourth root of y)

$\frac{8 y^{2}}{2 \sqrt[4]{y}}$

Step 1

Cancel the common factor of $8$ and $2$ .

Factor $2$ out of $8 y^{2}$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

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

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

Step 3

Combine and simplify the denominator.

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

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

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

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

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

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

Add $1$ and $3$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Step 4

Cancel the common factor of $y^{2}$ and $y$ .

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

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

Cancel the common factors.

Raise $y$ to the power of $1$ .

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

Factor $y$ out of $y^{1}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $4 y {\sqrt[4]{y}}^{3}$ by $1$ .

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

Step 5

Rewrite ${\sqrt[4]{y}}^{3}$ as ${(y^{3})}^{\frac{1}{4}}$ .

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

Simplify the Radical Expression (8y^2)/(2 fourth root of y)

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