What is e^{-2t}(e^{-t}-e^{-2t}) ?

The solution to e^{-2t}(e^{-t}-e^{-2t}) is (e^t-1)/(e^{4t)}

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simplify e^{-2t}(e^{-t}-e^{-2t})

simplify

e^{- 2 t} (e^{- t} - e^{- 2 t})

\frac{e ^{t} - 1}{e ^{4 t}}

Solution steps

e^{- 2 t} (e^{- t} - e^{- 2 t})

Apply exponent rule:

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

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

Multiply fractions:

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

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

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

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

Factor

e^{- t} - e^{- 2 t} : e^{- 2 t} (e^{t} - 1)

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

Cancel

\frac{e ^{- 2 t} ( e ^{t} - 1 )}{e ^{2 t}} : \frac{e ^{t} - 1}{e ^{4 t}}

= \frac{e ^{t} - 1}{e ^{4 t}}

12 x^{2} (24 x^{2})

(2.6 x 1 0^{(- 6)}) x (3 x 1 0^{(- 3)})

(\frac{x}{z})^{1.6} (y)^{1.6}

e^{- 158}

2.68 (1 0^{- 3})

What is e^{-2t}(e^{-t}-e^{-2t}) ?
The solution to e^{-2t}(e^{-t}-e^{-2t}) is (e^t-1)/(e^{4t)}