[tex]\it 5\cdot5^5\cdot5^3\cdot\ ...\ \cdot5^{50}=5^{1+2+3+\ ...\ +50}=5^{\frac{50\cdot51}{2}}=5^{25\cdot51}=5^{25\cdot17\cdot3}=125^{425}\\ \\ \\ 2^{2975}=2^{7\cdot425}=(2^7)^{425}=128^{425}\\ \\ \\ 128^{425}>125^{425}\Rightarrow 2^{2975}>5\cdot5^5\cdot5^3\cdot\ ...\ \cdot5^{50}[/tex]
Răspuns:
[tex]\bf 5 \cdot 5^{2} \cdot 5^{3} \cdot.... \cdot 5^{50} =5^{1 + 2 + 3 + .... + 50} =[/tex]
[tex]\bf 5^{50 \cdot 51:2 } = 5^{25 \cdot 51}=5^{1275} =\big(5^{3}\big)^{425}=\green{\underline{ \: 125^{425} \: }}[/tex]
[tex]\bf {2}^{2975} = \big(2^{7}\big)^{425}=\blue{\underline{~128^{425}~ }}[/tex]
[tex]\bf 128 > 125 \implies \red{ \boxed{ \bf {2}^{2975} \: > \: 5^{1275}}}[/tex]
