What is e^{-(x^2)/(a^2)}*(x^2)/(e^{x/a)} ?

The solution to e^{-(x^2)/(a^2)}*(x^2)/(e^{x/a)} is (x^2)/(e^{\frac{x^2+ax){a^2}}}

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simplify e^{-(x^2)/(a^2)}*(x^2)/(e^{x/a)}

simplify

e^{- \frac{x ^{2}}{a ^{2}}} \cdot \frac{x ^{2}}{e ^{\frac{x}{a}}}

\frac{x ^{2}}{e ^{\frac{x ^{2} + a x}{a ^{2}}}}

Solution steps

e^{- \frac{x ^{2}}{a ^{2}}} \frac{x ^{2}}{e ^{\frac{x}{a}}}

Apply exponent rule:

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

= \frac{1}{e ^{\frac{x ^{2}}{a ^{2}}}} \cdot \frac{x ^{2}}{e ^{\frac{x}{a}}}

Multiply fractions:

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

= \frac{1 \cdot x ^{2}}{e ^{\frac{x ^{2}}{a ^{2}}} e ^{\frac{x}{a}}}

Multiply:

1 \cdot x^{2} = x^{2}

= \frac{x ^{2}}{e ^{\frac{x ^{2}}{a ^{2}}} e ^{\frac{x}{a}}}

e^{\frac{x ^{2}}{a ^{2}}} e^{\frac{x}{a}} = e^{\frac{x ^{2}}{a ^{2}} + \frac{x}{a}}

= \frac{x ^{2}}{e ^{\frac{x ^{2}}{a ^{2}} + \frac{x}{a}}}

e^{\frac{x ^{2}}{a ^{2}} + \frac{x}{a}} = e^{\frac{x ^{2} + a x}{a ^{2}}}

= \frac{x ^{2}}{e ^{\frac{x ^{2} + x a}{a ^{2}}}}

2 e^{- t} (t + 1)

t \cdot (e^{- a t})^{n}

e^{3 x} \cdot e^{2 y} d x

- 0.0 5^{2} \cdot 4 \cdot 1 0^{- 7} \cdot \frac{1000}{0.04} \cdot \frac{1}{0.04}

e^{- a t} \cdot sin (wt) \cdot u (t - 1)

What is e^{-(x^2)/(a^2)}*(x^2)/(e^{x/a)} ?
The solution to e^{-(x^2)/(a^2)}*(x^2)/(e^{x/a)} is (x^2)/(e^{\frac{x^2+ax){a^2}}}