[tex]( {2 \sqrt{2}) }^{50} = {2}^{50} \times {2}^{25} = {2}^{75} = ({ {2}^{5} )}^{15} = {32}^{15} \\( {3 \sqrt{3} })^{30} = {3}^{30} \times {3}^{15} = {3}^{45} = ( { {3}^{3} )}^{15} = {27}^{15} \\( {2 \sqrt{2}) }^{50} > {(3 \sqrt{3}) }^{30} \\ | {3}^{45} - {2}^{75} | = {2}^{75} - {3}^{45} \\ {(3 \sqrt{3} )}^{30} + {(2 \sqrt{2} )}^{50} + {(2 \sqrt{2}) }^{50} - {(3 \sqrt{3} )}^{30} = 2 \times ( {2 \sqrt{2}) }^{50} = {2}^{75} \times 2 = {2}^{76} [/tex]
