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

The solution to (1/2 e^{x/2})(xe^{x/2}) is (e^xx)/2

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simplify (1/2 e^{x/2})(xe^{x/2})

simplify

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

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

Solution steps

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

Apply exponent rule:

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

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

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

Combine the fractions

\frac{x}{2} + \frac{x}{2} : x

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

Multiply fractions:

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

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

Multiply:

1 \cdot x = x

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

Multiply fractions:

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

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

0.08 \times 1 0^{- 3}

e^{- \frac{1}{8} (6)}

(ln (8 x) + 1) (8 x)^{x}

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