Question

Comparati numerele 128 la puterea 56 si 4 la puterea 223; 10 la puterea 100 si 100 la puterea 10; 7 la puterea 88 si 49 la puterea 45.

Answer 1

$1) 128^{56}= 2^{7*56}= 2^{392} \\4^{223}= 2^{2*223}= 2^{446} \\ 128^{56}\ \textless \ 4^{223} \\ \\ 2) 10^{100} ;100 ^{10}= 10^{2*10}= 10^{20} \\ 10^{100} \ \textgreater \ 100 ^{10} \\ \\ 3) 7^{88} ;49^{45}=7^{2*45}= 7^{90} ;7^{88} \ \textless \ 49^{45}$