What is e^{x/2}\times e^{x/2} ?

The solution to e^{x/2}\times e^{x/2} is e^x

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simplify e^{x/2}\times e^{x/2}

simplify

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

e^{x}

Solution steps

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

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

Combine the fractions

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

= e^{x}

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