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Popular >

simplify \sqrt[100]{81^{75}}

Solution

simplify

Solution

27

Solution steps

Apply radical rule:

= (8 1^{75})^{\frac{1}{100}}

Apply exponent rule:

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

= 8 1^{75 \cdot \frac{1}{100}}

75 \cdot \frac{1}{100} = \frac{3}{4}

= 8 1^{\frac{3}{4}}

Factor the number:

81 = 3^{4}

= (3^{4})^{\frac{3}{4}}

Apply exponent rule:

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

(3^{4})^{\frac{3}{4}} = 3^{4 \cdot \frac{3}{4}} = 3^{3}

= 3^{3}

Refine

= 27

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Frequently Asked Questions (FAQ)

What is \sqrt[100]{81^{75}} ?
The solution to \sqrt[100]{81^{75}} is 27