Basic Math Examples

P (25) = \frac{20^{25} e^{- 20}}{25 (25 - 1) (25 - 2) \cdot 3 \cdot 2 \cdot 1}

$P (25) = \frac{20^{25} e^{- 20}}{25 (25 - 1) (25 - 2) \cdot 3 \cdot 2 \cdot 1}$

Step 1

Simplify.

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Step 1.1

Rewrite the expression using the negative exponent rule

b^{- n} = \frac{1}{b^{n}}

$b^{- n} = \frac{1}{b^{n}}$ .

P (25) = \frac{20^{25} \frac{1}{e^{20}}}{25 (25 - 1) (25 - 2) \cdot 3 \cdot 2 \cdot 1}

$P (25) = \frac{20^{25} \frac{1}{e^{20}}}{25 (25 - 1) (25 - 2) \cdot 3 \cdot 2 \cdot 1}$

Step 1.2

Combine

20^{25}

$20^{25}$ and

\frac{1}{e^{20}}

$\frac{1}{e^{20}}$ .

P (25) = \frac{\frac{20^{25}}{e^{20}}}{25 (25 - 1) (25 - 2) \cdot 3 \cdot 2 \cdot 1}

$P (25) = \frac{\frac{20^{25}}{e^{20}}}{25 (25 - 1) (25 - 2) \cdot 3 \cdot 2 \cdot 1}$

Step 1.3

Subtract

1

$1$ from

25

$25$ .

P (25) = \frac{\frac{20^{25}}{e^{20}}}{25 \cdot 24 (25 - 2) \cdot 3 \cdot 2 \cdot 1}

$P (25) = \frac{\frac{20^{25}}{e^{20}}}{25 \cdot 24 (25 - 2) \cdot 3 \cdot 2 \cdot 1}$

Step 1.4

Multiply

25

$25$ by

24

$24$ .

P (25) = \frac{\frac{20^{25}}{e^{20}}}{600 (25 - 2) \cdot 3 \cdot 2 \cdot 1}

$P (25) = \frac{\frac{20^{25}}{e^{20}}}{600 (25 - 2) \cdot 3 \cdot 2 \cdot 1}$

Step 1.5

Subtract

2

$2$ from

25

$25$ .

P (25) = \frac{\frac{20^{25}}{e^{20}}}{600 \cdot 23 \cdot 3 \cdot 2 \cdot 1}

$P (25) = \frac{\frac{20^{25}}{e^{20}}}{600 \cdot 23 \cdot 3 \cdot 2 \cdot 1}$

Step 1.6

Multiply

600

$600$ by

23

$23$ .

P (25) = \frac{\frac{20^{25}}{e^{20}}}{13800 \cdot 3 \cdot 2 \cdot 1}

$P (25) = \frac{\frac{20^{25}}{e^{20}}}{13800 \cdot 3 \cdot 2 \cdot 1}$

Step 1.7

Multiply

13800

$13800$ by

3

$3$ .

P (25) = \frac{\frac{20^{25}}{e^{20}}}{41400 \cdot 2 \cdot 1}

$P (25) = \frac{\frac{20^{25}}{e^{20}}}{41400 \cdot 2 \cdot 1}$

Step 1.8

Multiply

41400

$41400$ by

2

$2$ .

P (25) = \frac{\frac{20^{25}}{e^{20}}}{82800 \cdot 1}

$P (25) = \frac{\frac{20^{25}}{e^{20}}}{82800 \cdot 1}$

Step 1.9

Multiply

82800

$82800$ by

1

$1$ .

P (25) = \frac{\frac{20^{25}}{e^{20}}}{82800}

$P (25) = \frac{\frac{20^{25}}{e^{20}}}{82800}$

Step 1.10

Multiply the numerator by the reciprocal of the denominator.

P (25) = \frac{20^{25}}{e^{20}} \cdot \frac{1}{82800}

$P (25) = \frac{20^{25}}{e^{20}} \cdot \frac{1}{82800}$

Step 1.11

Combine.

P (25) = \frac{20^{25} \cdot 1}{e^{20} \cdot 82800}

$P (25) = \frac{20^{25} \cdot 1}{e^{20} \cdot 82800}$

Step 1.12

Multiply

20^{25}

$20^{25}$ by

1

$1$ .

P (25) = \frac{20^{25}}{e^{20} \cdot 82800}

$P (25) = \frac{20^{25}}{e^{20} \cdot 82800}$

Step 1.13

Move

82800

$82800$ to the left of

e^{20}

$e^{20}$ .

P (25) = \frac{20^{25}}{82800 e^{20}}

$P (25) = \frac{20^{25}}{82800 e^{20}}$

P (25) = \frac{20^{25}}{82800 e^{20}}

$P (25) = \frac{20^{25}}{82800 e^{20}}$

Step 2

Divide each term in

P (25) = \frac{20^{25}}{82800 e^{20}}

$P (25) = \frac{20^{25}}{82800 e^{20}}$ by

25

$25$ and simplify.

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Step 2.1

Divide each term in

P (25) = \frac{20^{25}}{82800 e^{20}}

$P (25) = \frac{20^{25}}{82800 e^{20}}$ by

25

$25$ .

\frac{P (25)}{25} = \frac{\frac{20^{25}}{82800 e^{20}}}{25}

$\frac{P (25)}{25} = \frac{\frac{20^{25}}{82800 e^{20}}}{25}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of

25

$25$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{P \cdot 25}{25} = \frac{\frac{20^{25}}{82800 e^{20}}}{25}$

Step 2.2.1.2

Divide

$P$ by

$1$ .

$P = \frac{\frac{20^{25}}{82800 e^{20}}}{25}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply the numerator by the reciprocal of the denominator.

$P = \frac{20^{25}}{82800 e^{20}} \cdot \frac{1}{25}$

Step 2.3.2

Combine.

$P = \frac{20^{25} \cdot 1}{82800 e^{20} \cdot 25}$

Step 2.3.3

Multiply.

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Step 2.3.3.1

Multiply

$20^{25}$ by

$1$ .

$P = \frac{20^{25}}{82800 e^{20} \cdot 25}$

Step 2.3.3.2

Multiply

$25$ by

$82800$ .

$P = \frac{20^{25}}{2070000 e^{20}}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$P = \frac{20^{25}}{2070000 e^{20}}$

Decimal Form:

$P = 3.34110333 \cdot 10^{17}$