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Popular >

simplify sqrt((n/(1+n))^n)

Solution

simplify

(\frac{n}{1 + n})^{n}

Solution

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

Solution steps

(\frac{n}{1 + n})^{n}

Apply radical rule:

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

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

Apply exponent rule:

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

assuming

a \geq 0

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

Simplify

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

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

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

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Frequently Asked Questions (FAQ)

What is sqrt((n/(1+n))^n) ?
The solution to sqrt((n/(1+n))^n) is (n/(n+1))^{n/2}