Question

5) Calcule o valor de
$\sqrt[3]{9. \sqrt[3]{9. \sqrt[3]{9. \sqrt[3]{27} } } }$
me ajudem por favor!​

Answer 1

$\sqrt[a]{b^c}=b^{\frac{c}{a}}$

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$\sqrt[3]{9.\sqrt[3]{9.\sqrt[3]{9.\sqrt[3]{27}}}}\\\\\sqrt[3]{3^2.\sqrt[3]{3^2.\sqrt[3]{3^2.\sqrt[3]{3^3}}}}\\\\\sqrt[3]{3^2.\sqrt[3]{3^2.\sqrt[3]{3^2.3}}}\\\\\sqrt[3]{3^2.\sqrt[3]{3^2.\sqrt[3]{3^3}}}\\\\\sqrt[3]{3^2.\sqrt[3]{3^2.3}}\\\\\sqrt[3]{3^2.\sqrt[3]{3}}\\\\\sqrt[3]{3^2.3}\\\\\sqrt[3]{3^3}\\\\3$