Question

Comparați 5^8 cu 2^15+2*4^7
Ajutatima varog

Answer 1

[tex]5^8 ~?~2^{15}+2\times 4^7 \\ \\ 5^8 ~?~2^{15}+2\times \Big(2^2\Big)^7 \\ \\ 5^8 ~?~2^{15}+2\times 2^{2\times7} \\ \\ 5^8 ~?~2^{15}+2\times 2^{14} \\ \\ 5^8 ~?~2^{15}+ 2^{1+14} \\ \\ 5^8 ~?~2^{15}+ 2^{15} \\ \\ 5^8 ~?~2\times 2^{15} \\ \\ 5^8 ~?~2^{1+15} \\ \\ 5^8 ~?~2^{16} \\ \\ 5^8 ~?~2^{2\times 8} \\ \\ 5^8 ~?~\Big(2^2\Big)^8} \\ \\ \boxed{5^8 \ \textgreater \ 4^8} \\ \\ \Longrightarrow~~ \boxed{5^8 \ \textgreater \ 2^{15}+2\times 4^7}[/tex]