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Popular >

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

Solution

simplify

x^{x}

Solution

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

Solution steps

(x)^{x}

Apply radical rule:

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

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

Apply exponent rule:

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

assuming

a \geq 0

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

Simplify

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

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

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25 (73)

Frequently Asked Questions (FAQ)

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