Question

26. A expressão representada na figra adiante é equivalente a:

∛ a √a
----- ----
b b


PORFAVOR, AJUDEM

Answer 1

Vamos utilizar as seguintes propriedades:
$\sqrt[n]{a^{m}}=a^{\frac{m}{n}}\\ \\a=a^1\\ \\(a^n)^m=a^{n\cdot m}$

$\sqrt[3]{ \frac{a}{b} \sqrt{\frac{a}{b}} }= \sqrt[3]{ \big(\frac{a}{b}\big)^{1}\cdot \big(\frac{a}{b}\big)^{ \frac{1}{2} } }= \sqrt[3]{ \big(\frac{a}{b}\big)^{1+ \frac{1}{2}}} = \sqrt[3]{ \big(\frac{a}{b}\big)^{\frac{2}{2} + \frac{1}{2}}} = \sqrt[3]{ \big(\frac{a}{b}\big)^{\frac{3}{2}}} \\ \\= \Big[\big(\frac{a}{b}\big)^{\frac{3}{2}} \Big]^{ \frac{1}{3}} = \big(\frac{a}{b}\big)^{\frac{3}{2}\cdot \frac{1}{3}}= \big(\frac{a}{b}\big)^{\frac{3^{:3}}{6_{:3}}} = \big(\frac{a}{b}\big)^{\frac{1}{2}}= \sqrt{\frac{a}{b}}$