Question

Simplifique:
⁴√2²¹ • 3¹¹

Answer 1

$\sqrt[4]{2^{21}\cdot3^{11}} \\ = \sqrt[4]{2^{20+1}\cdot3^{8+3}}\\ =\sqrt[4]{2^{20}\cdot2^1\cdot3^{8}\cdot3^{3}} \\ =\sqrt[4]{2^{20}\cdot3^{8}\cdot2^1\cdot3^{3}} \\ =\sqrt[4]{2^{20}\cdot3^8}\cdot\sqrt[4]{2\cdot3^3}\\ =\sqrt[4]{2^{20}}\cdot\sqrt[4]{3^{8}}\cdot\sqrt[4]{2\cdot3^3}\\ =2^5\cdot{3^2\cdot\sqrt[4]{2\cdot27}\\ =32\cdot{9\cdot\sqrt[4]{54}\\ \\=288\sqrt[4]{54}$