Question

Resolva usando as propriedades:

Answer 1

$a)\ \sqrt{9\sqrt{3}}=\sqrt{\sqrt{9^2.3}}=\sqrt[4]{9^2.3}=\sqrt[4]{3^4.3}=\sqrt[4]{3^4.3}=3\sqrt[4]{3} \\ \\ \\ b)\ \sqrt{\sqrt{\sqrt{\sqrt[5]{\sqrt[4]{6}}}}}=\sqrt[160]{6} \\ \\ \\ c)\ (\sqrt[3]{5})^4=\sqrt[3]{5^4}=\sqrt[3]{5^3.5}=5\sqrt{5} \\ \\ \\ d)\ (\sqrt{a})^{-10}= \frac{1}{(\sqrt{a})^{10}}=\frac{1}{\sqrt{a^{10}}}=\frac{1}{\sqrt{a^2.a^2.a^2.a^2.a^2}}=\frac{1}{a.a.a.a.a}=\frac{1}{a^5} \\ \\ \\ e)\ \frac{\sqrt[3]{15}}{\sqrt[3]{3}}=\sqrt[3]{\frac{15}{3}}=\sqrt[3]{5}\\\\\\f)\ \frac{\sqrt[6]{100}}{\sqrt[6]{50}}=\sqrt[6]{\frac{100}{50}}=\sqrt[6]{2}\\\\\\g)\ \sqrt[3]{2}.\sqrt[3]{-90}=\sqrt[3]{2.(-90)}=\sqrt[3]{-180}$