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Popular >

simplify sqrt(n)^{sqrt(n)}

Solution

simplify

n^{n}

Solution

n^{\frac{n}{2}}

Solution steps

(n)^{n}

Apply radical rule:

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

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

Apply exponent rule:

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

assuming

a \geq 0

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

Simplify

\frac{1}{2} n : \frac{n}{2}

= n^{\frac{n}{2}}

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Frequently Asked Questions (FAQ)

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