Question

. O valor de (√√2√2 3 ) 8 é: a) 2√2² 3 b) 2 6 √2² 3 c) 2 d) 4 e) 8.

Answer 1

$O \ valor\ de\ \bigg( \sqrt[3]{\sqrt{2\sqrt{2} } } \bigg)^8 \ \acute{e}:\\\ a)\ 2\sqrt[3]{2^2}\\b)\ 2^6\cdot\sqrt[3]{2^2}\\c)\ 2\\d)\ 4\\e)\ 8$

$\bigg( \sqrt[3]{\sqrt{2\sqrt{2} } } \bigg)^8=\bigg( \sqrt[3]{\sqrt{\sqrt{2^1\cdot2^2} } } \bigg)^8=\Big( \sqrt[3\cdot2\cdot2]{2^{1+2}}\Big)^8\\\\\\=\Big( \sqrt[12]{2^3}\Big)^8=\sqrt[12]{2^{3\cdot8}}=\sqrt[12]{2^{24}} =2^{\frac{24}{12}}=2^2=4$