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Popular >

simplify \sqrt[9]{216^6}

Solution

simplify

Solution

36

Solution steps

Apply radical rule:

= (21 6^{6})^{\frac{1}{9}}

Apply exponent rule:

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

= 21 6^{6 \cdot \frac{1}{9}}

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

= 21 6^{\frac{2}{3}}

Factor the number:

216 = 6^{3}

= (6^{3})^{\frac{2}{3}}

Apply exponent rule:

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

(6^{3})^{\frac{2}{3}} = 6^{3 \cdot \frac{2}{3}} = 6^{2}

= 6^{2}

Refine

= 36

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Frequently Asked Questions (FAQ)

What is \sqrt[9]{216^6} ?
The solution to \sqrt[9]{216^6} is 36