Finite Math Examples

$\frac{{(9)}^{5}}{5!} \cdot e^{- 8}$

Step 1

Raise $9$ to the power of $5$ .

$\frac{59049}{5!} \cdot e^{- 8}$

Step 2

Simplify the denominator.

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Step 2.1

Expand $5!$ to $5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

$\frac{59049}{5 \cdot 4 \cdot 3 \cdot 2 \cdot 1} \cdot e^{- 8}$

Step 2.2

Multiply $5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

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Step 2.2.1

Multiply $5$ by $4$ .

$\frac{59049}{20 \cdot 3 \cdot 2 \cdot 1} \cdot e^{- 8}$

Step 2.2.2

Multiply $20$ by $3$ .

$\frac{59049}{60 \cdot 2 \cdot 1} \cdot e^{- 8}$

Step 2.2.3

Multiply $60$ by $2$ .

$\frac{59049}{120 \cdot 1} \cdot e^{- 8}$

Step 2.2.4

Multiply $120$ by $1$ .

$\frac{59049}{120} \cdot e^{- 8}$

Step 3

Cancel the common factor of $59049$ and $120$ .

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Step 3.1

Factor $3$ out of $59049$ .

$\frac{3 (19683)}{120} \cdot e^{- 8}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $3$ out of $120$ .

$\frac{3 \cdot 19683}{3 \cdot 40} \cdot e^{- 8}$

Step 3.2.2

Cancel the common factor.

$\frac{3 \cdot 19683}{3 \cdot 40} \cdot e^{- 8}$

Step 3.2.3

Rewrite the expression.

$\frac{19683}{40} \cdot e^{- 8}$

Step 4

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{19683}{40} \cdot \frac{1}{e^{8}}$

Step 5

Combine.

$\frac{19683 \cdot 1}{40 e^{8}}$

Step 6

Multiply $19683$ by $1$ .

$\frac{19683}{40 e^{8}}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{19683}{40 e^{8}}$

Decimal Form:

$0.16507277 \dots$