What is e^{-11.5}(11.5^{10})/(10!) ?

The solution to e^{-11.5}(11.5^{10})/(10!) is 0.11293…

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simplify e^{-11.5}(11.5^{10})/(10!)

simplify

e^{- 11.5} \frac{11. 5 ^{10}}{10 !}

0.11293 \dots

Solution steps

e^{- 11.5} \frac{11. 5 ^{10}}{10 !}

Apply exponent rule:

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

= \frac{1}{e ^{11.5}} \cdot \frac{11. 5 ^{10}}{10 !}

Multiply fractions:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{1 \cdot 11. 5 ^{10}}{e ^{11.5} \cdot 10 !}

Multiply:

1 \cdot 11. 5^{10} = 11. 5^{10}

= \frac{11. 5 ^{10}}{e ^{11.5} \cdot 10 !}

e^{11.5} \cdot 10! = 3628800 e^{11.5}

= \frac{11. 5 ^{10}}{3628800 e ^{11.5}}

e^{11.5} = 98715.77101 \dots

= \frac{11. 5 ^{10}}{3628800 \cdot 98715.77101 \dots}

11. 5^{10} = 40455577357.0791

= \frac{40455577357.0791}{3628800 \cdot 98715.77101 \dots}

Multiply the numbers:

3628800 \cdot 98715.77101 \dots = 358219789843.8475

= \frac{40455577357.0791}{358219789843.8475}

Divide the numbers:

\frac{40455577357.0791}{358219789843.8475} = 0.11293 \dots

= 0.11293 \dots

2^{n} \cdot e^{n}

\frac{1}{8} 0. 1^{- 2}

e^{- \frac{4}{9}}

\frac{2 2 ^{32}}{7 ^{32}}

What is e^{-11.5}(11.5^{10})/(10!) ?
The solution to e^{-11.5}(11.5^{10})/(10!) is 0.11293…