Simplify 3/( square root of 18xy^2)

$\frac{3}{\sqrt{18 x y^{2}}}$

Step 1

Simplify the denominator.

Rewrite $18 x y^{2}$ as ${(3 y)}^{2} \cdot (2 x)$ .

Factor $9$ out of $18$ .

$\frac{3}{\sqrt{9 (2) x y^{2}}}$

Rewrite $9$ as $3^{2}$ .

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

Move $x$ .

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

Move $2$ .

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

Rewrite $3^{2} y^{2}$ as ${(3 y)}^{2}$ .

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

Add parentheses.

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

Pull terms out from under the radical.

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

Step 2

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Multiply $\frac{1}{y \sqrt{2 x}}$ by $\frac{\sqrt{2 x}}{\sqrt{2 x}}$ .

$\frac{1}{y \sqrt{2 x}} \cdot \frac{\sqrt{2 x}}{\sqrt{2 x}}$

Step 4

Combine and simplify the denominator.

Multiply $\frac{1}{y \sqrt{2 x}}$ by $\frac{\sqrt{2 x}}{\sqrt{2 x}}$ .

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

Move $\sqrt{2 x}$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Step 5

Move $2$ to the left of $y$ .

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

Simplify 3/( square root of 18xy^2)

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