Răspuns: [tex]\color{CC0000}\Large\boxed{\bf N~ se~ termina~ in~ 24~ de~ zerouri}[/tex]
Explicație pas cu pas:
Salutare!
[tex]\large\bf N = 16^{12}\cdot27^{8}\cdot625^{6}[/tex]
[tex]\large\bf N = (2^{4})^{12}\cdot(3^{3})^{8}\cdot(5^{4})^{6}[/tex]
[tex]\large\bf N = 2^{4\cdot 12}\cdot3^{3\cdot8}\cdot5^{4\cdot6}[/tex]
[tex]\large\bf N = 2^{48}\cdot3^{24}\cdot5^{24}[/tex]
[tex]\large\bf N = 10^{24}\cdot2^{24}\cdot3^{24}[/tex]
[tex]\large\boxed{\bf 10^{24}\cdot6^{24}\implies N~ se~ termina~ in~ 24~ de~ zerouri}[/tex]
Varianta D)
P.S.: Cred ca varianta aceasta ai bifat-o la olimpiada locala din 20 februarie 2021.
Mult succes!
#copaceibrainly
