Finite Math Examples

$\frac{2 x}{5 y} \cdot \frac{15 y^{3} x^{4}}{4 x}$

Step 1

Combine.

$\frac{2 x (15 y^{3} x^{4})}{5 y (4 x)}$

Step 2

Multiply $x$ by $x^{4}$ by adding the exponents.

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Step 2.1

Move $x^{4}$ .

$\frac{2 (x^{4} x) (15 y^{3})}{5 y (4 x)}$

Step 2.2

Multiply $x^{4}$ by $x$ .

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Step 2.2.1

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

$\frac{2 (x^{4} x^{1}) (15 y^{3})}{5 y (4 x)}$

Step 2.2.2

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

$\frac{2 x^{4 + 1} (15 y^{3})}{5 y (4 x)}$

$\frac{2 x^{4 + 1} (15 y^{3})}{5 y (4 x)}$

Step 2.3

Add $4$ and $1$ .

$\frac{2 x^{5} (15 y^{3})}{5 y (4 x)}$

$\frac{2 x^{5} (15 y^{3})}{5 y (4 x)}$

Step 3

Cancel the common factor of $2$ and $4$ .

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Step 3.1

Factor $2$ out of $2 x^{5} (15 y^{3})$ .

$\frac{2 (x^{5} (15 y^{3}))}{5 y (4 x)}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $5 y (4 x)$ .

$\frac{2 (x^{5} (15 y^{3}))}{2 (5 y (2 x))}$

Step 3.2.2

Cancel the common factor.

$\frac{2 (x^{5} (15 y^{3}))}{2 (5 y (2 x))}$

Step 3.2.3

Rewrite the expression.

$\frac{x^{5} (15 y^{3})}{5 y (2 x)}$

$\frac{x^{5} (15 y^{3})}{5 y (2 x)}$

$\frac{x^{5} (15 y^{3})}{5 y (2 x)}$

Step 4

Cancel the common factor of $x^{5}$ and $x$ .

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Step 4.1

Factor $x$ out of $x^{5} (15 y^{3})$ .

$\frac{x (x^{4} (15 y^{3}))}{5 y (2 x)}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $x$ out of $5 y (2 x)$ .

$\frac{x (x^{4} (15 y^{3}))}{x (5 y \cdot (2))}$

Step 4.2.2

Cancel the common factor.

$\frac{x (x^{4} (15 y^{3}))}{x (5 y \cdot (2))}$

Step 4.2.3

Rewrite the expression.

$\frac{x^{4} (15 y^{3})}{5 y \cdot (2)}$

$\frac{x^{4} (15 y^{3})}{5 y \cdot (2)}$

$\frac{x^{4} (15 y^{3})}{5 y \cdot (2)}$

Step 5

Cancel the common factor of $15$ and $5$ .

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Step 5.1

Factor $5$ out of $x^{4} (15 y^{3})$ .

$\frac{5 (x^{4} (3 y^{3}))}{5 y \cdot (2)}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $5$ out of $5 y \cdot (2)$ .

$\frac{5 (x^{4} (3 y^{3}))}{5 (y \cdot (2))}$

Step 5.2.2

Cancel the common factor.

$\frac{5 (x^{4} (3 y^{3}))}{5 (y \cdot (2))}$

Step 5.2.3

Rewrite the expression.

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

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

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

Step 6

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

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Step 6.1

Factor $y$ out of $x^{4} (3 y^{3})$ .

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

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $y$ out of $y \cdot (2)$ .

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

Step 6.2.2

Cancel the common factor.

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

Step 6.2.3

Rewrite the expression.

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

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

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

Step 7

Move $3$ to the left of $x^{4}$ .

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

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$