Colégio Naval 1977 ⇒ Questão 01 - CN - 1977 Tópico resolvido

[petrasMOD]

O valor de [tex3]\sqrt[3]{16\sqrt{8}}.\sqrt[6]{0,125}[/tex3] é:
a) 2[tex3]\sqrt{8}[/tex3] b) 4[tex3]\sqrt[3]{4}[/tex3] c) [tex3]4\sqrt{2}[/tex3]d) 2[tex3]\sqrt[3]{2}[/tex3] e) [tex3]4\sqrt[6]{2}[/tex3]

[petrasMOD]

[tex3]\mathsf{\sqrt[3]{\sqrt{16^2.2^3}}.\sqrt[6]{0,5^3}\\
\sqrt[6]{{(2^4)}^2.2^3}.\sqrt[6]{(\frac{1}{2})^3}\\
\sqrt[6]{2^{11}}.\sqrt[6]{2^{-3}}=\sqrt[6]{2^8} = 2^{\frac{8}{6}} = 2^{\frac{4}{3}}\\
\sqrt[3]{2^4} = \sqrt[3]{2^3.2} = \boxed{2\sqrt[3]{2}_{//}}}

[/tex3]