What is 200(1-e^{-1})(2e^{-2(400)}) ?

The solution to 200(1-e^{-1})(2e^{-2(400)}) is (400(e-1))/(e^{801)}

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simplify 200(1-e^{-1})(2e^{-2(400)})

simplify

200 (1 - e^{- 1}) (2 e^{- 2 (400)})

\frac{400 ( e - 1 )}{e ^{801}}

Solution steps

200 (1 - e^{- 1}) (2 e^{- 2 (400)})

Apply exponent rule:

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

= 200 \cdot 2 \cdot \frac{1}{e ^{2 \cdot 400}} (- e^{- 1} + 1)

Multiply the numbers:

2 \cdot 400 = 800

= 200 \cdot 2 \cdot \frac{1}{e ^{800}} (- e^{- 1} + 1)

Multiply fractions:

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

= \frac{1 \cdot 200 ( 1 - e ^{- 1} ) \cdot 2}{e ^{800}}

Multiply the numbers:

1 \cdot 200 \cdot 2 = 400

= \frac{400 ( - e ^{- 1} + 1 )}{e ^{800}}

Apply exponent rule:

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

= \frac{400 ( - \frac{1}{e} + 1 )}{e ^{800}}

Join

1 - \frac{1}{e} : \frac{e - 1}{e}

= \frac{400 \cdot \frac{e - 1}{e}}{e ^{800}}

Multiply

400 \cdot \frac{e - 1}{e} : \frac{400 ( e - 1 )}{e}

= \frac{\frac{400 ( e - 1 )}{e}}{e ^{800}}

Apply the fraction rule:

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

= \frac{( e - 1 ) \cdot 400}{e e ^{800}}

e e^{800} = e^{801}

= \frac{400 ( e - 1 )}{e ^{801}}

(43) (610)

e^{- l n (2)}

n^{2} (n + 1)^{2} (n + 2)^{2}

4.63 \cdot 1 0^{- 3}

5.48 \cdot 1 0^{- 5}

What is 200(1-e^{-1})(2e^{-2(400)}) ?
The solution to 200(1-e^{-1})(2e^{-2(400)}) is (400(e-1))/(e^{801)}