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Popular >

simplify \sqrt[66]{27^{20}}

Solution

simplify

Solution

3^{\frac{10}{11}}

+1

Decimal Notation

2.71485 \dots

Solution steps

Apply radical rule:

= (2 7^{20})^{\frac{1}{66}}

Apply exponent rule:

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

= 2 7^{20 \cdot \frac{1}{66}}

20 \cdot \frac{1}{66} = \frac{10}{33}

= 2 7^{\frac{10}{33}}

Factor the number:

27 = 3^{3}

= (3^{3})^{\frac{10}{33}}

Apply exponent rule:

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

(3^{3})^{\frac{10}{33}} = 3^{3 \cdot \frac{10}{33}} = 3^{\frac{10}{11}}

= 3^{\frac{10}{11}}

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Frequently Asked Questions (FAQ)

What is \sqrt[66]{27^{20}} ?
The solution to \sqrt[66]{27^{20}} is 3^{10/11}