Question

Determine o valor de X, sabendo-se que
x=(2 √2 √2 √2 √2 √2).(^16 √2)

Answer 1

Explicação passo-a-passo:

$x=(2\sqrt{2\sqrt{2\sqrt{2\sqrt{2} } } } ).\sqrt[16]{2} \\ \\ x=\sqrt{2.2^2\sqrt{2\sqrt{2\sqrt{2} } } } .\sqrt[16]{2} \\ \\ x=(\sqrt{2^3\sqrt{2\sqrt{2\sqrt{2} } } } ).\sqrt[16]{2} \\ \\ x=(\sqrt{\sqrt{2.2^6\sqrt{2\sqrt{2} } } } ).\sqrt[16]{2} \\ \\ x=(\sqrt{\sqrt{2^7\sqrt{2\sqrt{2} } } } ).\sqrt[16]{2} \\ \\ x=\sqrt{\sqrt{\sqrt{2.2^{14}\sqrt{2} } } } ).\sqrt[16]{2} \\ \\ x=\sqrt{\sqrt{\sqrt{2^{15}\sqrt{2} } } } ) .\sqrt[16]{2} \\ \\ x=\sqrt{\sqrt{\sqrt{\sqrt{2.2^{30}} } } }) .\sqrt[16]{2}$

$x=\sqrt{\sqrt{\sqrt{\sqrt{2^{31}} } } } ).\sqrt[16]{2} \\ \\ x=\sqrt[2.2.2.2]{2^{31}} .\sqrt[16]{2} \\ \\ x=\sqrt[16]{2^{31}} .\sqrt[16]{2} \\ \\ x=\sqrt[16]{2^{31}.2} \\ \\ x=\sqrt[16]{2^{32}} \\ \\ x=2^2\\ \\ \fbox{ x=4 }$