Răspuns:
[tex] \large \bf( - 2)^{1} \cdot ( - 2)^{2} \cdot( - 2)^{3} \cdot ( - 2)^{4} \cdot ....\cdot ( - 2)^{100} : {4}^{2525} = [/tex]
[tex] \large \bf( - 2)^{1 + 2 + 3 + 4 + .... + 100} : {4}^{2525} = [/tex]
Aplicam suma lui Gauss pentru a afla exponentul lui (-2)
100 • (100 + 1) : 2 = 50 • 101 = 5050
[tex]\large \bf( - 2)^{5050} : {4}^{2525} = [/tex]
[tex]\large \bf( - 2)^{5050} : (2^{2})^{2525} = [/tex]
[tex]\large \bf 2^{5050} : 2^{2 \cdot 2525} = [/tex]
[tex]\large \bf 2^{5050} : 2^{5050} = [/tex]
[tex]\large \bf 2^{5050 - 5050}={2}^{0} = \boxed{ \bf 1}[/tex]
#copaceibrainly
