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

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

Step 1

Simplify the denominator.

Rewrite $6 x^{3}$ as $x^{2} \cdot (6 x)$ .

Factor out $x^{2}$ .

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

Reorder $6$ and $x^{2}$ .

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

Add parentheses.

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

Pull terms out from under the radical.

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

Step 2

Cancel the common factor of $x$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{\sqrt{6 x}}$

Step 3

Multiply $\frac{1}{\sqrt{6 x}}$ by $\frac{\sqrt{6 x}}{\sqrt{6 x}}$ .

$\frac{1}{\sqrt{6 x}} \cdot \frac{\sqrt{6 x}}{\sqrt{6 x}}$

Step 4

Combine and simplify the denominator.

Multiply $\frac{1}{\sqrt{6 x}}$ by $\frac{\sqrt{6 x}}{\sqrt{6 x}}$ .

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

Raise $\sqrt{6 x}$ to the power of $1$ .

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

Raise $\sqrt{6 x}$ to the power of $1$ .

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

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

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

Add $1$ and $1$ .

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

Rewrite ${\sqrt{6 x}}^{2}$ as $6 x$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6 x}$ as ${(6 x)}^{\frac{1}{2}}$ .

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

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

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