Question

Simplifique o radical:
(√32)^5

Answer 1

$\left(\sqrt{32}\right)^{5}\\ \\ =\left(\sqrt{2^{5}} \right )^{5}\\ \\ =\left(2^{\,^{5}\!\!\!\diagup\!\!_{2}}\right)^{5}\\ \\ =2^{\,^{5 \,\cdot\, 5}\!\!\!\diagup\!\!_{2}}\\ \\ =2^{\,^{25}\!\!\!\diagup\!\!_{2}}\\ \\ =2^{\,^{24}\!\!\!\diagup\!\!_{2}+\,^{1}\!\!\!\diagup\!\!_{2}}\\ \\ =2^{12+\,^{1}\!\!\!\diagup\!\!_{2}}\\ \\ =2^{12}\cdot 2^{\,^{1}\!\!\!\diagup\!\!_{2}}\\ \\ =2^{12}\cdot \sqrt{2}\\ \\ =4\,096\sqrt{2}\\ \\ \\ \boxed{\left(\sqrt{32}\right)^{5}=4\,096\sqrt{2}}$