Question

Gente essa é a ultima questão ajudem! vms lá gente somente essa ai acabou!

Answer 1

Olá!

    Temos:

         $\dfrac{3^{\frac{1}{2}}+3^{(-\frac{2}{3})}}{3^{\frac{1}{2}} \cdot 3^{(-\frac{2}{3})}}= \dfrac{3^{\frac{1}{2}}+\dfrac{1}{3^{\frac{2}{3}}}}{3^{\frac{1}{2}} \cdot 3^{(-\frac{2}{3})}}= \dfrac{\frac{3^\frac{2}{3} \cdot 3^{\frac{1}{2}}+1}{3^\frac{2}{3}}}{3^{\frac{1}{2}} \cdot 3^{(-\frac{2}{3})}}= \\ \\ \\ =\dfrac{\frac{3^{\frac{7}{6}}+1}{3^{\frac{2}{3}}}}{3^{\frac{1}{2}} \cdot 3^{(-\frac{2}{3})}} =\dfrac{3^{\frac{7}{6}}+1}{3^{\frac{2}{3}}}} \cdot \dfrac{1}{3^{\frac{1}{2}} \cdot 3^{(-\frac{2}{3})}}$

    Continuando,

    $\dfrac{3^{\frac{7}{6}}+1}{3^{\frac{2}{3}}}} \cdot \dfrac{1}{3^{\frac{1}{2}} \cdot 3^{(-\frac{2}{3})}}= \dfrac{3^{\frac{7}{6}}+1}{3^{\frac{2}{3}} \cdot 3^{(-\frac{2}{3})} \cdot 3^{\frac{1}{2}}}= \\ \\ \\ =\dfrac{3^{\frac{7}{6}}+1}{3^{\frac{1}{2}}}= \dfrac{3^{\frac{7}{6}}}{3^{\frac{1}{2}}}+\dfrac{1}{3^{\frac{1}{2}}}= 3^{\frac{2}{3}}+3^{(-\frac{1}{2})}$


Bons estudos!