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Popular >

simplify (sqrt(2))^n

Solution

simplify

(2)^{n}

Solution

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

Solution steps

(2)^{n}

Apply radical rule:

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

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

Apply exponent rule:

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

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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