\[\begin{array}{l} {\text{Проверьте верность равенства:}} \hfill \\ {\text{45}}{{\text{1}}^4} + {573^4} + {677^4} + {1002^4} = {11099^3}. \hfill \\ \end{array}\]

\[\begin{array}{l} {\text{Проверьте верность равенства:}} \hfill \\ {\text{62}}{{\text{3}}^4} + {749^4} + {822^4} + {1003^4} = {12459^3}. \hfill \\ \end{array}\]

\[\begin{array}{l} {\text{Упростите:}} \hfill \\ \sqrt[5]{{232 + 164\sqrt 2 }} + \sqrt[5]{{232 - 164\sqrt 2 }}. \hfill \\ \end{array}\]