Question 211274
*[Tex \LARGE \sqrt[3]{\sqrt{\frac{512}{343}}}]


*[Tex \LARGE \sqrt[3]{\left(\frac{512}{343}\right)^{\frac{1}{2}}}]


*[Tex \LARGE \left(\left(\frac{512}{343}\right)^{\frac{1}{2}}\right)^{\frac{1}{3}}]


*[Tex \LARGE \left(\frac{512}{343}\right)^{\frac{1}{2}\cdot\frac{1}{3}}]


*[Tex \LARGE \left(\frac{512}{343}\right)^{\frac{1}{3}\cdot\frac{1}{2}}]


*[Tex \LARGE \left(\left(\frac{512}{343}\right)^{\frac{1}{3}}\right)^{\frac{1}{2}}]


*[Tex \LARGE \left(\sqrt[3]{\frac{512}{343}}\right)^{\frac{1}{2}}]


*[Tex \LARGE \left(\frac{\sqrt[3]{512}}{\sqrt[3]{343}}\right)^{\frac{1}{2}}]


*[Tex \LARGE \left(\frac{\sqrt[3]{8^3}}{\sqrt[3]{7^3}}\right)^{\frac{1}{2}}]


*[Tex \LARGE \left(\frac{8}{7}\right)^{\frac{1}{2}}]


*[Tex \LARGE \sqrt{\frac{8}{7}}]


*[Tex \LARGE \frac{\sqrt{8}}{\sqrt{7}}]


*[Tex \LARGE \frac{\sqrt{8}\cdot\sqrt{7}}{\sqrt{7}\cdot\sqrt{7}}]


*[Tex \LARGE \frac{\sqrt{4\cdot2}\cdot\sqrt{7}}{7}]


*[Tex \LARGE \frac{\sqrt{4}\cdot\sqrt{2}\cdot\sqrt{7}}{7}]


*[Tex \LARGE \frac{2\cdot\sqrt{2}\cdot\sqrt{7}}{7}]


*[Tex \LARGE \frac{2\cdot\sqrt{2\cdot7}}{7}]


*[Tex \LARGE \frac{2\cdot\sqrt{14}}{7}]



Answer: *[Tex \LARGE \sqrt[3]{\sqrt{\frac{512}{343}}}=\frac{2\cdot\sqrt{14}}{7}]