Algebra Examples

$\frac{4 y}{\sqrt{2 x^{4} y}}$

Step 1

Simplify the denominator.

Tap for more steps...

Step 1.1

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

Tap for more steps...

Step 1.1.1

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

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

Step 1.1.2

Reorder $2$ and ${(x^{2})}^{2}$ .

$\frac{4 y}{\sqrt{{(x^{2})}^{2} \cdot 2 y}}$

Step 1.1.3

Add parentheses.

$\frac{4 y}{\sqrt{{(x^{2})}^{2} \cdot (2 y)}}$

Step 1.2

Pull terms out from under the radical.

$\frac{4 y}{x^{2} \sqrt{2 y}}$

Step 2

Multiply $\frac{4 y}{x^{2} \sqrt{2 y}}$ by $\frac{\sqrt{2 y}}{\sqrt{2 y}}$ .

$\frac{4 y}{x^{2} \sqrt{2 y}} \cdot \frac{\sqrt{2 y}}{\sqrt{2 y}}$

Step 3

Combine and simplify the denominator.

Tap for more steps...

Step 3.1

Multiply $\frac{4 y}{x^{2} \sqrt{2 y}}$ by $\frac{\sqrt{2 y}}{\sqrt{2 y}}$ .

$\frac{4 y \sqrt{2 y}}{x^{2} \sqrt{2 y} \sqrt{2 y}}$

Step 3.2

Move $\sqrt{2 y}$ .

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

Step 3.3

Raise $\sqrt{2 y}$ to the power of $1$ .

$\frac{4 y \sqrt{2 y}}{x^{2} ({\sqrt{2 y}}^{1} \sqrt{2 y})}$

Step 3.4

Raise $\sqrt{2 y}$ to the power of $1$ .

$\frac{4 y \sqrt{2 y}}{x^{2} ({\sqrt{2 y}}^{1} {\sqrt{2 y}}^{1})}$

Step 3.5

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

$\frac{4 y \sqrt{2 y}}{x^{2} {\sqrt{2 y}}^{1 + 1}}$

Step 3.6

Add $1$ and $1$ .

$\frac{4 y \sqrt{2 y}}{x^{2} {\sqrt{2 y}}^{2}}$

Step 3.7

Rewrite ${\sqrt{2 y}}^{2}$ as $2 y$ .

Tap for more steps...

Step 3.7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2 y}$ as ${(2 y)}^{\frac{1}{2}}$ .

$\frac{4 y \sqrt{2 y}}{x^{2} {({(2 y)}^{\frac{1}{2}})}^{2}}$

Step 3.7.2

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

$\frac{4 y \sqrt{2 y}}{x^{2} {(2 y)}^{\frac{1}{2} \cdot 2}}$

Step 3.7.3

Combine $\frac{1}{2}$ and $2$ .

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

Step 3.7.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.7.4.1

Cancel the common factor.

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

Step 3.7.4.2

Rewrite the expression.

$\frac{4 y \sqrt{2 y}}{x^{2} {(2 y)}^{1}}$

Step 3.7.5

Simplify.

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

Step 4

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

Tap for more steps...

Step 4.1

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

$\frac{2 (2 y \sqrt{2 y})}{x^{2} (2 y)}$

Step 4.2

Cancel the common factors.

Tap for more steps...

Step 4.2.1

Factor $2$ out of $x^{2} (2 y)$ .

$\frac{2 (2 y \sqrt{2 y})}{2 (x^{2} (y))}$

Step 4.2.2

Cancel the common factor.

$\frac{2 (2 y \sqrt{2 y})}{2 (x^{2} (y))}$

Step 4.2.3

Rewrite the expression.

$\frac{2 y \sqrt{2 y}}{x^{2} (y)}$

Step 5

Cancel the common factor of $y$ .

Tap for more steps...

Step 5.1

Cancel the common factor.

$\frac{2 y \sqrt{2 y}}{x^{2} y}$

Step 5.2

Rewrite the expression.

$\frac{2 \sqrt{2 y}}{x^{2}}$