Finite Math Examples

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

Step 1

Combine.

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

Step 2

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 2.1

Move $x$ .

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

Step 2.2

Multiply $x$ by $x^{2}$ .

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Step 2.2.1

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

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

Step 2.2.2

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

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

Step 2.3

Add $1$ and $2$ .

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

Step 3

Multiply $y$ by $y^{2}$ by adding the exponents.

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Step 3.1

Move $y^{2}$ .

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

Step 3.2

Multiply $y^{2}$ by $y$ .

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Step 3.2.1

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

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

Step 3.2.2

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

$\frac{2 x^{3} y^{2 + 1} \cdot 3}{3 x y \cdot 2}$

Step 3.3

Add $2$ and $1$ .

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

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

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

Step 5

Cancel the common factor of $x^{3}$ and $x$ .

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Step 5.1

Factor $x$ out of $x^{3} y^{3} \cdot 3$ .

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

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $x$ out of $3 x y$ .

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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

Step 6

Cancel the common factor of $y^{3}$ and $y$ .

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Step 6.1

Factor $y$ out of $x^{2} y^{3} \cdot 3$ .

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

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $y$ out of $3 y$ .

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

Step 6.2.2

Cancel the common factor.

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

Step 6.2.3

Rewrite the expression.

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

Step 7

Cancel the common factor of $3$ .

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Step 7.1

Cancel the common factor.

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

Step 7.2

Divide $x^{2} y^{2}$ by $1$ .

$x^{2} y^{2}$