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Popular >

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

Solution

simplify

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

Solution

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

Solution steps

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

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

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

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

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

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

Popular Examples

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0.5 \cdot 5

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e^{- 2.5} \frac{( 2.5 ) ^{3}}{6}

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5.67 \cdot 1 0^{- 8} \cdot 0.8 \cdot 1.5 \cdot (30 7^{4} - 28 3^{4})

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0.0013 (e^{\frac{25 + 273}{478}})^{- 3.9213}

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(2 e^{- j^{0.3}}) \cdot (3 e^{j^{0.4}})

Frequently Asked Questions (FAQ)

What is xe^x*e^{-x/2} ?
The solution to xe^x*e^{-x/2} is e^{x/2}x