Trigonometry Examples

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

Step 1

Simplify the denominator.

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Step 1.1

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

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Step 1.1.1

Reorder $3$ and $x^{2}$ .

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

Step 1.1.2

Add parentheses.

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

Step 1.2

Pull terms out from under the radical.

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

Step 2

Multiply $\frac{3}{x \sqrt{3 y}}$ by $\frac{\sqrt{3 y}}{\sqrt{3 y}}$ .

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

Step 3

Combine and simplify the denominator.

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Step 3.1

Multiply $\frac{3}{x \sqrt{3 y}}$ by $\frac{\sqrt{3 y}}{\sqrt{3 y}}$ .

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

Step 3.2

Move $\sqrt{3 y}$ .

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

Step 3.3

Raise $\sqrt{3 y}$ to the power of $1$ .

$\frac{3 \sqrt{3 y}}{x ({\sqrt{3 y}}^{1} \sqrt{3 y})}$

Step 3.4

Raise $\sqrt{3 y}$ to the power of $1$ .

$\frac{3 \sqrt{3 y}}{x ({\sqrt{3 y}}^{1} {\sqrt{3 y}}^{1})}$

Step 3.5

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

$\frac{3 \sqrt{3 y}}{x {\sqrt{3 y}}^{1 + 1}}$

Step 3.6

Add $1$ and $1$ .

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

Step 3.7

Rewrite ${\sqrt{3 y}}^{2}$ as $3 y$ .

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Step 3.7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 y}$ as ${(3 y)}^{\frac{1}{2}}$ .

$\frac{3 \sqrt{3 y}}{x {({(3 y)}^{\frac{1}{2}})}^{2}}$

Step 3.7.2

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

$\frac{3 \sqrt{3 y}}{x {(3 y)}^{\frac{1}{2} \cdot 2}}$

Step 3.7.3

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

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

Step 3.7.4

Cancel the common factor of $2$ .

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Step 3.7.4.1

Cancel the common factor.

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

Step 3.7.4.2

Rewrite the expression.

$\frac{3 \sqrt{3 y}}{x {(3 y)}^{1}}$

Step 3.7.5

Simplify.

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

Step 4

Cancel the common factor of $3$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

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

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