What is (1-e^{-3})*e^{-2} ?

The solution to (1-e^{-3})*e^{-2} is (e^3-1)/(e^5)

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simplify (1-e^{-3})*e^{-2}

simplify

(1 - e^{- 3}) \cdot e^{- 2}

\frac{e ^{3} - 1}{e ^{5}}

Decimal Notation

0.12859 \dots

Solution steps

(1 - e^{- 3}) e^{- 2}

Apply exponent rule:

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

= \frac{1}{e ^{2}} (- e^{- 3} + 1)

Multiply fractions:

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

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

1 \cdot (1 - e^{- 3}) = 1 - e^{- 3}

= \frac{1 - e ^{- 3}}{e ^{2}}

Apply exponent rule:

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

= \frac{1 - \frac{1}{e ^{3}}}{e ^{2}}

Join

1 - \frac{1}{e ^{3}} : \frac{e ^{3} - 1}{e ^{3}}

= \frac{\frac{e ^{3} - 1}{e ^{3}}}{e ^{2}}

Apply the fraction rule:

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

= \frac{e ^{3} - 1}{e ^{3} e ^{2}}

e^{3} e^{2} = e^{5}

= \frac{e ^{3} - 1}{e ^{5}}

e^{- t} (cos (wt) - 2 sin (w) t)

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2.83 \cdot 1 0^{- 9}