Question

Se 4 elevado 16 . 5 elevado 25 = a . 10 elevado n com 1≤a∠10 então n é igual :

Answer 1

$4^{16}.5^{25}=a.10^{n} \\ \\ (2^{2})^{32}.5^{25}=a.10^{n} \\ \\ 2^{32}.5^{25}=a.10^{n} \\ \\ 2^{25}.2^{7}.5^{25} = a.10^{n} \\ \\ 2^{7}.(2.5)^{25}=a.10^{n} \\ \\ 2^{7}.10^{25}=a.10^{n} \\ \\ 128.10^{25}=a.10^{n} \\ \\ 1,28.10^{27}=a.10^{n} \\ \\ a = 1,28 \\ \\ 10^{27}=10^{n} \\ \\ n = 27$

Espero ter ajudado.