Question

In cate zerouri se termina numarul: 4 la puterea a 7 ori 5 la puterea a 12 ori 3 la puterea a 8?
Ajutati-ma urgent!
Dau coroana!

Answer 1

   
[tex]4^7 \times 5^{12} \times 3^8 = \\ \\ =(2^2)^7 \times 5^{12} \times 3^8 = \\ \\ =2^{2\times 7} \times 5^{12} \times 3^8 = \\ \\ =2^{14} \times 5^{12} \times 3^8 = \\ \\ =2^{2+12} \times 5^{12} \times 3^8 = \\ \\ =2^2 \times 2^{12} \times 5^{12} \times 3^8 = \\ \\ = 2^2 \times 3^8 \times 2^{12} \times 5^{12} = \\ \\ = 2^2 \times 3^8 \times (2\times 5)^{12} = \\ \\ = 2^2 \times 3^8 \times 10^{12} ~~~~~\Longrightarrow ~~ \boxed{12~\text{zerouri}} [/tex]