Question

(Colégio Naval - RJ) O valor de ³√16√8 * 6^√0,125 é:
a) 2√8
b) 4³√4
c) 4√2
d) 4³√2

Answer 1

.
$\sqrt[3]{16} . \sqrt{8} . \sqrt[6]{0,125} = \\ \\ \sqrt[3]{2^4} . \sqrt{2^3} . \sqrt[6]{0,125} = \\ mmc(3,2,6)=6~~~igualando~~os~~indices \\ \\ \sqrt[6]{2^8.2^9.0,125} = \\ \\ \sqrt[6]{2^{17}.0,125} = \\ \\ 2^2 \sqrt[6]{2^5.0,125} = \\ \\ 4 \sqrt[6]{32.0,125} = \\ \\ 4 \sqrt[6]{4} =4 \sqrt[6]{2^2} =4 \sqrt[3]{2}$

R: Letra D