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Popular >

simplify sqrt(9^n)

Solution

simplify

9^{n}

Solution

3^{n}

Solution steps

9^{n}

Apply radical rule:

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

= (9^{n})^{\frac{1}{2}}

Apply exponent rule:

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

= 9^{n \frac{1}{2}}

Simplify

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

= 9^{\frac{n}{2}}

Factor the number:

9 = 3^{2}

= (3^{2})^{\frac{n}{2}}

Apply exponent rule:

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

(3^{2})^{\frac{n}{2}} = 3^{2 \cdot \frac{n}{2}} = 3^{n}

= 3^{n}

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Frequently Asked Questions (FAQ)

What is sqrt(9^n) ?
The solution to sqrt(9^n) is 3^n