Finite Math Examples

$\frac{3 y}{\sqrt{9 x^{3} y^{4}}}$

Step 1

Simplify the denominator.

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Step 1.1

Rewrite $9 x^{3} y^{4}$ as ${(3 x y^{2})}^{2} x$ .

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Step 1.1.1

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

$\frac{3 y}{\sqrt{3^{2} x^{3} y^{4}}}$

Step 1.1.2

Factor out $x^{2}$ .

$\frac{3 y}{\sqrt{3^{2} (x^{2} x) y^{4}}}$

Step 1.1.3

Rewrite $y^{4}$ as ${(y^{2})}^{2}$ .

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

Step 1.1.4

Move $x$ .

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

Step 1.1.5

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

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

Step 1.2

Pull terms out from under the radical.

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

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $3$ .

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Step 2.1.1

Cancel the common factor.

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

Step 2.1.2

Rewrite the expression.

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

Step 2.2

Cancel the common factor of $y$ and $y^{2}$ .

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Step 2.2.1

Raise $y$ to the power of $1$ .

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

Step 2.2.2

Factor $y$ out of $y^{1}$ .

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

Step 2.2.3

Cancel the common factors.

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Step 2.2.3.1

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

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

Step 2.2.3.2

Cancel the common factor.

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

Step 2.2.3.3

Rewrite the expression.

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

Step 3

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

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

Step 4

Combine and simplify the denominator.

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Step 4.1

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

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

Step 4.2

Move $\sqrt{x}$ .

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

Step 4.3

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

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

Step 4.4

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

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

Step 4.5

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

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

Step 4.6

Add $1$ and $1$ .

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

Step 4.7

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

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Step 4.7.1

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

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

Step 4.7.2

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

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

Step 4.7.3

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

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

Step 4.7.4

Cancel the common factor of $2$ .

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Step 4.7.4.1

Cancel the common factor.

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

Step 4.7.4.2

Rewrite the expression.

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

Step 4.7.5

Simplify.

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

Step 5

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

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Step 5.1

Move $x$ .

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

Step 5.2

Multiply $x$ by $x$ .

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