[tex]\bf 5 \cdot 5^{2} \cdot 5^{3} \cdot.... \cdot 5^{50} =5^{1 + 2 + 3 + .... + 50} =[/tex]
Aplicăm suma lui Gauss pentru a afla exponentul lui 5
[tex]\bf 5^{50 \cdot 51:2 } = 5^{25 \cdot 51}=5^{1275} =\big(5^{3}\big)^{425}=\purple{\underline{ \: 125^{425} \: }}[/tex]
[tex]\bf {2}^{2975} = \big(2^{7}\big)^{425}=\blue{\underline{~128^{425}~ }}[/tex]
[tex]\bf 128 > 125 \implies \pink{ \boxed{ \bf {2}^{2975} \: > \: 5^{1275}}}[/tex]
