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

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

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

simplify

e^{\frac{3 x}{2}} (\frac{1}{2} e^{- x})

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

Solution steps

e^{\frac{3 x}{2}} (\frac{1}{2} e^{- x})

Apply exponent rule:

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

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

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

Multiply:

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

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

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

(3 x^{\frac{2}{3}}) (3 x^{\frac{1}{3}})

2 (214)

(a + 3) \cdot (a - 3)

2000 \cdot 9.7 \cdot 1 0^{- 7}

(5 x^{2}) (2 y^{2})

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