Algebra Examples

$\frac{6 y}{\sqrt{2 x}}$

Step 1

Multiply $\frac{6 y}{\sqrt{2 x}}$ by $\frac{\sqrt{2 x}}{\sqrt{2 x}}$ .

$\frac{6 y}{\sqrt{2 x}} \cdot \frac{\sqrt{2 x}}{\sqrt{2 x}}$

Step 2

Combine and simplify the denominator.

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Step 2.1

Multiply $\frac{6 y}{\sqrt{2 x}}$ by $\frac{\sqrt{2 x}}{\sqrt{2 x}}$ .

$\frac{6 y \sqrt{2 x}}{\sqrt{2 x} \sqrt{2 x}}$

Step 2.2

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

$\frac{6 y \sqrt{2 x}}{{\sqrt{2 x}}^{1} \sqrt{2 x}}$

Step 2.3

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

$\frac{6 y \sqrt{2 x}}{{\sqrt{2 x}}^{1} {\sqrt{2 x}}^{1}}$

Step 2.4

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

$\frac{6 y \sqrt{2 x}}{{\sqrt{2 x}}^{1 + 1}}$

Step 2.5

Add $1$ and $1$ .

$\frac{6 y \sqrt{2 x}}{{\sqrt{2 x}}^{2}}$

Step 2.6

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

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Step 2.6.1

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

$\frac{6 y \sqrt{2 x}}{{({(2 x)}^{\frac{1}{2}})}^{2}}$

Step 2.6.2

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

$\frac{6 y \sqrt{2 x}}{{(2 x)}^{\frac{1}{2} \cdot 2}}$

Step 2.6.3

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

$\frac{6 y \sqrt{2 x}}{{(2 x)}^{\frac{2}{2}}}$

Step 2.6.4

Cancel the common factor of $2$ .

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Step 2.6.4.1

Cancel the common factor.

$\frac{6 y \sqrt{2 x}}{{(2 x)}^{\frac{2}{2}}}$

Step 2.6.4.2

Rewrite the expression.

$\frac{6 y \sqrt{2 x}}{{(2 x)}^{1}}$

Step 2.6.5

Simplify.

$\frac{6 y \sqrt{2 x}}{2 x}$

Step 3

Cancel the common factor of $6$ and $2$ .

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Step 3.1

Factor $2$ out of $6 y \sqrt{2 x}$ .

$\frac{2 (3 y \sqrt{2 x})}{2 x}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $2 x$ .

$\frac{2 (3 y \sqrt{2 x})}{2 (x)}$

Step 3.2.2

Cancel the common factor.

$\frac{2 (3 y \sqrt{2 x})}{2 x}$

Step 3.2.3

Rewrite the expression.

$\frac{3 y \sqrt{2 x}}{x}$