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Popular >

simplify e^{-2t}*(-e^{-6t})

Solution

simplify

e^{- 2 t} \cdot (- e^{- 6 t})

Solution

- \frac{1}{e ^{8 t}}

Solution steps

e^{- 2 t} (- e^{- 6 t})

Apply exponent rule:

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

= \frac{1}{e ^{2 t}} (- e^{- 6 t})

Remove parentheses:

(- a) = - a

= - \frac{1}{e ^{2 t}} e^{- 6 t}

Multiply fractions:

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

= - \frac{1 \cdot e ^{- 6 t}}{e ^{2 t}}

Multiply:

1 \cdot e^{- 6 t} = e^{- 6 t}

= - \frac{e ^{- 6 t}}{e ^{2 t}}

Apply exponent rule:

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

\frac{e ^{- 6 t}}{e ^{2 t}} = e^{- 6 t - 2 t} = e^{- 8 t}

= - \frac{1}{e ^{8 t}}

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Frequently Asked Questions (FAQ)

What is e^{-2t}*(-e^{-6t}) ?
The solution to e^{-2t}*(-e^{-6t}) is -1/(e^{8t)}