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Popular >

simplify \sqrt[10]{243^8}

Solution

simplify

Solution

81

Solution steps

Apply radical rule:

= (24 3^{8})^{\frac{1}{10}}

Apply exponent rule:

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

= 24 3^{8 \cdot \frac{1}{10}}

8 \cdot \frac{1}{10} = \frac{4}{5}

= 24 3^{\frac{4}{5}}

Factor the number:

243 = 3^{5}

= (3^{5})^{\frac{4}{5}}

Apply exponent rule:

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

(3^{5})^{\frac{4}{5}} = 3^{5 \cdot \frac{4}{5}} = 3^{4}

= 3^{4}

Refine

= 81

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Frequently Asked Questions (FAQ)

What is \sqrt[10]{243^8} ?
The solution to \sqrt[10]{243^8} is 81