What is (e^{(3x^2)/2})/(e^{(x^2)/2)} ?

The solution to (e^{(3x^2)/2})/(e^{(x^2)/2)} is e^{x^2}

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simplify (e^{(3x^2)/2})/(e^{(x^2)/2)}

simplify

\frac{e ^{\frac{3 x ^{2}}{2}}}{e ^{\frac{x ^{2}}{2}}}

e^{x^{2}}

Solution steps

\frac{e ^{\frac{3 x ^{2}}{2}}}{e ^{\frac{x ^{2}}{2}}}

Apply exponent rule:

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

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

Combine the fractions

\frac{3 x ^{2}}{2} - \frac{x ^{2}}{2} : x^{2}

= e^{x^{2}}

- e^{- 3 x} \cdot e^{3 x}

(2 x 1 0^{- 2}) (6.28 x 1 0^{9})

((1 + \frac{x}{360})^{4} (1 + \frac{3 x}{360})^{3})^{4}

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

What is (e^{(3x^2)/2})/(e^{(x^2)/2)} ?
The solution to (e^{(3x^2)/2})/(e^{(x^2)/2)} is e^{x^2}