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

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

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

simplify

x^{x^{x}}

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

Solution steps

(x)^{(x)^{x}}

Apply radical rule:

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

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

Apply exponent rule:

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

assuming

a \geq 0

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

Simplify

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

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

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

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

e^{- l n (x - 2)}

680 \cdot 6.65 \cdot 1 0^{- 3}

(6 ab c) (5 a^{3} c^{2})

e^{- 3 x} \cdot e^{4 x}

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