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Popular >

simplify e^{-x}*1/2 e^{x/2}

Solution

simplify

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

Solution

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

Solution steps

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

Apply exponent rule:

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

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

Multiply:

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

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

Apply exponent rule:

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

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

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

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Frequently Asked Questions (FAQ)

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