Finite Math Examples

$\frac{{(8)}^{6}}{6!} \cdot e^{- 8}$

Step 1

Raise $8$ to the power of $6$ .

$\frac{262144}{6!} \cdot e^{- 8}$

Step 2

Simplify the denominator.

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Step 2.1

Expand $6!$ to $6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

$\frac{262144}{6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1} \cdot e^{- 8}$

Step 2.2

Multiply $6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

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Step 2.2.1

Multiply $6$ by $5$ .

$\frac{262144}{30 \cdot 4 \cdot 3 \cdot 2 \cdot 1} \cdot e^{- 8}$

Step 2.2.2

Multiply $30$ by $4$ .

$\frac{262144}{120 \cdot 3 \cdot 2 \cdot 1} \cdot e^{- 8}$

Step 2.2.3

Multiply $120$ by $3$ .

$\frac{262144}{360 \cdot 2 \cdot 1} \cdot e^{- 8}$

Step 2.2.4

Multiply $360$ by $2$ .

$\frac{262144}{720 \cdot 1} \cdot e^{- 8}$

Step 2.2.5

Multiply $720$ by $1$ .

$\frac{262144}{720} \cdot e^{- 8}$

Step 3

Cancel the common factor of $262144$ and $720$ .

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Step 3.1

Factor $16$ out of $262144$ .

$\frac{16 (16384)}{720} \cdot e^{- 8}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $16$ out of $720$ .

$\frac{16 \cdot 16384}{16 \cdot 45} \cdot e^{- 8}$

Step 3.2.2

Cancel the common factor.

$\frac{16 \cdot 16384}{16 \cdot 45} \cdot e^{- 8}$

Step 3.2.3

Rewrite the expression.

$\frac{16384}{45} \cdot e^{- 8}$

Step 4

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

$\frac{16384}{45} \cdot \frac{1}{e^{8}}$

Step 5

Combine.

$\frac{16384 \cdot 1}{45 e^{8}}$

Step 6

Multiply $16384$ by $1$ .

$\frac{16384}{45 e^{8}}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{16384}{45 e^{8}}$

Decimal Form:

$0.12213821 \dots$