Question

A questão está na imagem.

Answer 1

$\sqrt{\sqrt{\sqrt[3]{\frac{2^{40}-2^{39}-2^{38}}{(\frac{1}{2})^{-2}}}}}$

$\sqrt{\sqrt{\sqrt[3]{\frac{2^{38}(2^2-2^1-1)}{2^2}}}}}$

$\sqrt{\sqrt{\sqrt[3]{\frac{2^{38}(4-2-1)}{2^2}}}}$

$\sqrt{\sqrt{\sqrt[3]{\frac{2^{38}\cdot1}{2^2}}}}$

$\sqrt{\sqrt{\sqrt[3]{\frac{2^{38}}{2^2}}}}$

$\sqrt{\sqrt{\sqrt[3]{2^{38-2}}}}$

$\sqrt{\sqrt{\sqrt[3]{2^{36}}}}$

$\sqrt{\sqrt{(2^{36})^{\frac{1}{3}}}$

$\sqrt{((2^{36})^{\frac{1}{3}})^{\frac{1}{2}}$

$(((2^{36})^{\frac{1}{3}})^{\frac{1}{2}})^{\frac{1}{2}}$

$2^{\frac{36}{\frac{1}{3}\cdot\frac{1}{2}\cdot\frac{1}{2}}}$

$2^{\frac{36}{12}}$

$2^3$

Pronto, a resposta é a letra C.