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

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

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simplify e^{-t}((e^t(x-y))/2)

simplify

e^{- t} (\frac{e ^{t} ( x - y )}{2})

\frac{x - y}{2}

Solution steps

e^{- t} (\frac{e ^{t} ( x - y )}{2})

Apply exponent rule:

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

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

Multiply fractions:

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

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

Cancel the common factor:

e^{t}

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

1 \cdot (x - y) = x - y

= \frac{x - y}{2}

4 (0.5)^{- 2}

0.5 \cdot 1 0^{- 1}

- 4.8456 \cdot e^{- 0.0673 (3)}

0.5 \cdot 1 0^{- 7}

\frac{6.7 5 ^{5}}{5 !} \cdot e^{- 6.75}