What is sqrt(xe)^{sqrt(x)} ?

The solution to sqrt(xe)^{sqrt(x)} is (ex)^{(sqrt(x))/2}

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simplify sqrt(xe)^{sqrt(x)}

simplify

x e^{x}

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

Solution steps

(x e)^{x}

Apply radical rule:

a = a^{\frac{1}{2}}

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

Apply exponent rule:

(a^{b})^{c} = a^{b c},

assuming

a \geq 0

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

Simplify

\frac{1}{2} x : \frac{x}{2}

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

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

4.74 \cdot 1 0^{- 6}

(3 m^{2}) (m^{3} t^{3}) (2 m t^{2})

- e^{- x} \cdot (- 2) e^{- 2 x}

19 x (m x^{m - 1})

What is sqrt(xe)^{sqrt(x)} ?
The solution to sqrt(xe)^{sqrt(x)} is (ex)^{(sqrt(x))/2}