What is (1+e^{-5})^{-1} ?

The solution to (1+e^{-5})^{-1} is (e^5)/(e^5+1)

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simplify (1+e^{-5})^{-1}

simplify

(1 + e^{- 5})^{- 1}

\frac{e ^{5}}{e ^{5} + 1}

Solution steps

(1 + e^{- 5})^{- 1}

Apply exponent rule:

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

= \frac{1}{( 1 + e ^{- 5} )}

Apply exponent rule:

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

= \frac{1}{1 + \frac{1}{e ^{5}}}

Join

1 + \frac{1}{e ^{5}} : \frac{e ^{5} + 1}{e ^{5}}

= \frac{1}{\frac{e ^{5} + 1}{e ^{5}}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{e ^{5}}{e ^{5} + 1}

\frac{e ^{t}}{e ^{- 2 t}}

1 0^{- 5} \cdot \frac{0.011}{0.2}

(20.25 \cdot 1 0^{- 3})^{2} (50.5 \cdot 1 0^{- 3})

2 e^{- t} \cdot e^{- t}

(4 a) (3 a^{3})