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

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

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

simplify

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

- \frac{1}{2}

Decimal Notation

- 0.5

Solution steps

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

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e^{- 2 t} e^{2 t} = e^{- 2 t + 2 t}

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

Add similar elements:

- 2 t + 2 t = 0

= (- \frac{1}{2}) e^{0}

Apply rule

a^{0} = 1, a \neq = 0

e^{0} = 1

= 1 \cdot (- \frac{1}{2})

Remove parentheses:

(- a) = - a

= - \frac{1}{2} \cdot 1

Multiply:

\frac{1}{2} \cdot 1 = \frac{1}{2}

= - \frac{1}{2}

27.1 (1 0^{- 1})

5 a \times 2 a \times (a^{3} - 3 a^{2} + a)

1.7 x 1 0^{- 5}

e^{- x} x