Question

Alguma pode me ajudar pfvr

Answer 1

$x=\dfrac{4^{4}}{\sqrt[4]{4}} = \dfrac{4^{4}}{4^{\frac{1}{4}}} = 4^{4-\frac{1}{4}} = 4^{3,75} = 4^{\frac{15}{4}} = \sqrt[4]{4^{15}}$

Então:

$\sqrt[4]{4^{15}} = \sqrt[4]{4^{4}\cdot4^{4}\cdot4^{4}\cdot4^{3}} = 4\cdot4\cdot4\cdot\sqrt[4]{4^{3}} = 64\cdot\sqrt[4]{4\cdot4\cdot4}=\\ 64\cdot\sqrt[4]{2\cdot2\cdot2\cdot2\cdot2\cdot2}=64\cdot\sqrt[4]{2^{4}\cdot2^{2}} =64\cdot2\cdot2^{\frac{2}{4}}= 128\cdot2^{\frac{1}{2}}=\\ 128\cdot\sqrt{2}$