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Popular >

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

Solution

simplify

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

Solution

- \frac{1}{e ^{2 t}}

Solution steps

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

Apply exponent rule:

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

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

Remove parentheses:

(- a) = - a

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

Multiply fractions:

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

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

Multiply:

1 \cdot e^{- t} = e^{- t}

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

Apply exponent rule:

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

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

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

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Frequently Asked Questions (FAQ)

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