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Popular >

simplify \sqrt[5]{(243^4)}

Solution

simplify

Solution

81

Solution steps

Apply radical rule:

= (24 3^{4})^{\frac{1}{5}}

Apply exponent rule:

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

= 24 3^{4 \cdot \frac{1}{5}}

4 \cdot \frac{1}{5} = \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[5]{(243^4)} ?
The solution to \sqrt[5]{(243^4)} is 81