What is 1/2 e^{-x/2}*1/3 e^{(t-x)/3} ?

The solution to 1/2 e^{-x/2}*1/3 e^{(t-x)/3} is (e^{(2t-5x)/6})/(6)

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simplify 1/2 e^{-x/2}*1/3 e^{(t-x)/3}

simplify

\frac{1}{2} e^{- \frac{x}{2}} \cdot \frac{1}{3} e^{\frac{t - x}{3}}

\frac{e ^{\frac{2 t - 5 x}{6}}}{6}

Solution steps

\frac{1}{2} e^{- \frac{x}{2}} \frac{1}{3} e^{\frac{t - x}{3}}

Apply exponent rule:

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

= \frac{1}{2} \cdot \frac{1}{3} e^{\frac{t - x}{3}} \frac{1}{e ^{\frac{x}{2}}}

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 1 \cdot e ^{\frac{t - x}{3}}}{2 e ^{\frac{x}{2}} \cdot 3}

Refine

= \frac{e ^{\frac{t - x}{3}}}{6 e ^{\frac{x}{2}}}

Apply exponent rule:

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

\frac{e ^{\frac{t - x}{3}}}{e ^{\frac{x}{2}}} = e^{\frac{t - x}{3} - \frac{x}{2}} = e^{\frac{2 t - 5 x}{6}}

= \frac{e ^{\frac{2 t - 5 x}{6}}}{6}

(2 \cdot 1 0^{- 7}) (34) (\frac{10.69 \cdot 1 0 ^{- 3}}{0.02})

10 - x x + 10

π (27.5 mm)^{2} (54 mm)

\frac{8 9 ^{25}}{9 0 ^{25}}

k e^{- k} \cdot e^{- k}

What is 1/2 e^{-x/2}*1/3 e^{(t-x)/3} ?
The solution to 1/2 e^{-x/2}*1/3 e^{(t-x)/3} is (e^{(2t-5x)/6})/(6)