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

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

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simplify (-1/2 e^t)(e^{-2t})

simplify

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

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

Solution steps

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

Apply exponent rule:

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

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

Remove parentheses:

(- a) = - a

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

Multiply fractions:

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

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

Multiply:

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

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

Apply exponent rule:

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

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

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

+ (- e^{- x})

(4 x^{5}) (3 x^{3})

(6.1 \cdot 1 0^{6}) \cdot (2 \cdot 1 0^{- 5})

5.72 \cdot 1 0^{- 3}

2^{(- 3)} \cdot 2