Question

Se x = 11, então \sqrt[5]{x^{15}} é igual a:

Answer 1

$\Huge\boxed{\begin{array}{l}\underline{\rm Pot\hat encia\,de\,pot\hat encia}\\\sf a^{m\cdot n}=(a^m)^n\\\underline{\rm Propriedade\,do\,radical\,aritm\acute etico}\\\sf \sqrt[\sf n]{\sf a^n}=a\end{array}}$

$\Large\boxed{\begin{array}{l}\sf\sqrt[\sf5]{\sf x^{15}}=\sqrt[\sf5]{\sf x^{3\cdot5}}=\sqrt[\sf5]{\sf (x^3)^5}=x^3\\\sf quando\,x=11\,teremos\\\sf 11^3=1331\end{array}}$