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Popular >

simplify \sqrt[9]{27^5}

Solution

simplify

Solution

3 \cdot 3^{\frac{2}{3}}

+1

Solution steps

Apply radical rule:

= (2 7^{5})^{\frac{1}{9}}

Apply exponent rule:

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

= 2 7^{5 \cdot \frac{1}{9}}

5 \cdot \frac{1}{9} = \frac{5}{9}

= 2 7^{\frac{5}{9}}

2 7^{\frac{5}{9}} = 3^{\frac{5}{3}}

= 3^{\frac{5}{3}}

3^{\frac{5}{3}} = 3 \cdot 3^{\frac{2}{3}}

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

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Frequently Asked Questions (FAQ)

What is \sqrt[9]{27^5} ?
The solution to \sqrt[9]{27^5} is 3*3^{2/3}