Simplify 6/( square root of 2x^3)

$\frac{6}{\sqrt{2 x^{3}}}$

Simplify the denominator.

Rewrite $2 x^{3}$ as $x^{2} \cdot (2 x)$ .

Factor out $x^{2}$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

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

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

Combine and simplify the denominator.

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

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

Move $\sqrt{2 x}$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x$ .

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

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

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

$\frac{2 (3 \sqrt{2 x})}{x^{2} \cdot 2}$

Cancel the common factors.

Factor $2$ out of $x^{2} \cdot 2$ .

$\frac{2 (3 \sqrt{2 x})}{2 \cdot x^{2}}$

Cancel the common factor.

$\frac{2 (3 \sqrt{2 x})}{2 \cdot x^{2}}$

Rewrite the expression.

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

Simplify 6/( square root of 2x^3)

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