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Popular >

simplify \sqrt[33]{27^2}

Solution

simplify

Solution

3^{\frac{2}{11}}

+1

Decimal Notation

1.22109 \dots

Solution steps

Apply radical rule:

= (2 7^{2})^{\frac{1}{33}}

Apply exponent rule:

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

= 2 7^{2 \cdot \frac{1}{33}}

2 \cdot \frac{1}{33} = \frac{2}{33}

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

Factor the number:

27 = 3^{3}

= (3^{3})^{\frac{2}{33}}

Apply exponent rule:

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

(3^{3})^{\frac{2}{33}} = 3^{3 \cdot \frac{2}{33}} = 3^{\frac{2}{11}}

= 3^{\frac{2}{11}}

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Frequently Asked Questions (FAQ)

What is \sqrt[33]{27^2} ?
The solution to \sqrt[33]{27^2} is 3^{2/11}