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

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

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

simplify

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

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

Solution steps

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

Apply exponent rule:

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

= e^{\frac{3 x}{2}} \frac{1}{e ^{x}}

Multiply fractions:

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

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

Multiply:

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

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

Apply exponent rule:

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

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

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

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