$\it{6}^{\,\it{4}}+ \it{5}^{\,\it{4}}+ \it{3}^{\,\it{4}}+ \it{2}^{\,\it{4}}+ \it{1}^{\,\it{4}}= \it{2019}$
$\it{2}^{\,\it{11}}- \it{2}^{\,\it{4}}- \it{2}^{\,\it{3}}- \it{2}^{\,\it{2}}- \it{2}^{\,\it{0}}= \it{2019}$
$\it{3}^{\,\it{7}}- \it{3}^{\,\it{5}}+ \it{3}^{\,\it{4}}- \it{3}^{\,\it{2}}+ \it{3}^{\,\it{1}}= \it{2019}$
$\it{5}^{\,\it{5}}- \it{4}^{\,\it{5}}- \it{3}^{\,\it{4}}- \it{1}^{\,\it{4}}= \it{2019}$
$\it{7}^{\,\it{4}}- \it{6}^{\,\it{3}}- \it{5}^{\,\it{3}}- \it{4}^{\,\it{3}}+ \it{3}^{\,\it{3}}- \it{2}^{\,\it{2}}= \it{2019}$
$\it{2}^{\,\it{10}}+ \it{2}^{\,\it{9}}+ \it{2}^{\,\it{8}}+ \it{2}^{\,\it{7}}+ \it{2}^{\,\it{6}}+ \it{2}^{\,\it{5}}+ \it{2}^{\,\it{4}}- \it{2}^{\,\it{3}}- \it{2}^{\,\it{2}}- \it{2}^{\,\it{1}}+ \it{2}^{\,\it{0}}= \it{2019}$