Question Number 44444 by peter frank last updated on 29/Sep/18
$${simplify}\:\:\:\:\sqrt{\left(\mathrm{4}{x}^{\mathrm{2}} {y}\right)^{\frac{\mathrm{2}}{\mathrm{3}}} +\left(\mathrm{8}{x}^{\mathrm{2}} {y}^{\mathrm{2}} \right)^{\mathrm{4}} } \\ $$
Answered by tanmay.chaudhury50@gmail.com last updated on 29/Sep/18
$$\sqrt{\left(\mathrm{2}^{\mathrm{2}} {x}^{\mathrm{2}} {y}\right)^{\frac{\mathrm{2}}{\mathrm{3}}} +\left(\mathrm{2}^{\mathrm{3}} {x}^{\mathrm{2}} {y}^{\mathrm{2}} \right)^{\mathrm{4}} } \\ $$$$=\sqrt{\mathrm{2}^{\frac{\mathrm{4}}{\mathrm{3}}} {x}^{\frac{\mathrm{4}}{\mathrm{3}}} {y}^{\frac{\mathrm{2}}{\mathrm{3}}} +\mathrm{2}^{\mathrm{12}} {x}^{\mathrm{8}} {y}^{\mathrm{8}} } \\ $$$$=\sqrt{\mathrm{2}^{\frac{\mathrm{4}}{\mathrm{3}}} {x}^{\frac{\mathrm{4}}{\mathrm{3}}} {y}^{\frac{\mathrm{2}}{\mathrm{3}}} \left(\mathrm{1}+\mathrm{2}^{\frac{\mathrm{32}}{\mathrm{3}}} {x}^{\frac{\mathrm{20}}{\mathrm{3}}} {y}^{\frac{\mathrm{22}}{\mathrm{3}}} \right)} \\ $$$$=\mathrm{2}^{\frac{\mathrm{2}}{\mathrm{3}}} {x}^{\frac{\mathrm{2}}{\mathrm{3}}} {y}^{\frac{\mathrm{1}}{\mathrm{3}}} ×\sqrt{\mathrm{1}+\mathrm{2}^{\frac{\mathrm{32}}{\mathrm{3}}} {x}^{\frac{\mathrm{20}}{\mathrm{3}}} {y}^{\frac{\mathrm{22}}{\mathrm{3}}} } \\ $$