Question

Calculando

a\cdot\sqrt{a^{-1}\sqrt{a^{-1}\sqrt{a^{-1}}}}

obtém-se:

a) \sqrt[6]{\frac{1}{a}}
b) 4a^{-1}
c) a^{-1}
d) \sqrt[8]{a}
e) \sqrt{a^{-1}}

Answer 1

$a\cdot\sqrt{a^{-1}\sqrt{a^{-1}\sqrt{a^{-1}}}}\\\\a\cdot a^{-1/2}\cdot a^{-1/4}\cdot a^{-1/8}\\\\a^{1-1/2-1/4-1/8}\\\\a^{(8-4-2-1)/8}\\\\a^{1/8}~~ou~~~\sqrt[8]{a}$