Question

A expressão √a √a³ / ³√a² . ⁴√a é equivalente?

Answer 1

$\dfrac{\sqrt{a}\cdot \,^{3}\!\!\! \sqrt{a}}{\,^{3}\!\!\!\sqrt{a^2}\cdot \,^{4}\!\!\!\sqrt{a}}\\\\\\ =\dfrac{a^{1/2}\cdot a^{1/3}}{a^{2/3}\cdot a^{1/4}}\\\\\\ =\dfrac{a^{(1/2)+(1/3)}}{a^{(2/3)+(1/4)}}\\\\\\ =\dfrac{a^{(3/6)+(2/6)}}{a^{(8/12)+(3/12)}}\\\\\\ =\dfrac{a^{5/6}}{a^{11/12}}$

$a^{(5/6)-(11/12)}\\\\ =a^{(10/12)-(11/12)}\\\\ =a^{-1/12}\\\\ =\dfrac{1}{a^{1/12}}\\\\\\ =\dfrac{1}{\,^{12}\!\!\!\!\sqrt{a}}$


Bons estudos! :-)