Finite Math Examples

$\frac{15 \cdot 14 \cdot 13 \cdot 12 \cdot 11 \cdot 10 \cdot 9}{15^{6}}$

Step 1

Cancel the common factor of $15$ and $15^{6}$ .

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Step 1.1

Factor $15$ out of $15 \cdot 14 \cdot 13 \cdot 12 \cdot 11 \cdot 10 \cdot 9$ .

$\frac{15 (14 \cdot 13 \cdot 12 \cdot 11 \cdot 10 \cdot 9)}{15^{6}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $15$ out of $15^{6}$ .

$\frac{15 (14 \cdot 13 \cdot 12 \cdot 11 \cdot 10 \cdot 9)}{15 \cdot 15^{5}}$

Step 1.2.2

Cancel the common factor.

$\frac{15 (14 \cdot 13 \cdot 12 \cdot 11 \cdot 10 \cdot 9)}{15 \cdot 15^{5}}$

Step 1.2.3

Rewrite the expression.

$\frac{14 \cdot 13 \cdot 12 \cdot 11 \cdot 10 \cdot 9}{15^{5}}$

Step 2

Simplify the numerator.

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Step 2.1

Multiply $14$ by $13$ .

$\frac{182 \cdot 12 \cdot 11 \cdot 10 \cdot 9}{15^{5}}$

Step 2.2

Multiply $182$ by $12$ .

$\frac{2184 \cdot 11 \cdot 10 \cdot 9}{15^{5}}$

Step 2.3

Multiply $2184$ by $11$ .

$\frac{24024 \cdot 10 \cdot 9}{15^{5}}$

Step 2.4

Multiply $24024$ by $10$ .

$\frac{240240 \cdot 9}{15^{5}}$

Step 2.5

Multiply $240240$ by $9$ .

$\frac{2162160}{15^{5}}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Raise $15$ to the power of $5$ .

$\frac{2162160}{759375}$

Step 3.2

Cancel the common factor of $2162160$ and $759375$ .

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Step 3.2.1

Factor $135$ out of $2162160$ .

$\frac{135 (16016)}{759375}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $135$ out of $759375$ .

$\frac{135 \cdot 16016}{135 \cdot 5625}$

Step 3.2.2.2

Cancel the common factor.

$\frac{135 \cdot 16016}{135 \cdot 5625}$

Step 3.2.2.3

Rewrite the expression.

$\frac{16016}{5625}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{16016}{5625}$

Decimal Form:

$2.8472\overline{8}$

Mixed Number Form:

$2 \frac{4766}{5625}$