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Popular >

simplify \sqrt[9]{27^6}

Solution

simplify

Solution

9

Solution steps

Apply radical rule:

= (2 7^{6})^{\frac{1}{9}}

Apply exponent rule:

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

= 2 7^{6 \cdot \frac{1}{9}}

6 \cdot \frac{1}{9} = \frac{2}{3}

= 2 7^{\frac{2}{3}}

Factor the number:

27 = 3^{3}

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

Apply exponent rule:

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

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

= 3^{2}

Refine

= 9

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Frequently Asked Questions (FAQ)

What is \sqrt[9]{27^6} ?
The solution to \sqrt[9]{27^6} is 9