Question

ordoneaza crescator
2^712 5^305 si 11^203

Answer 1

$2^{712}=2^5 \cdot 2^{707}=32 \cdot (2^7)^{101}=32 \cdot 128^{101} . \\ \\ 5^{305}=5^2 \cdot 5^{303}=25 \cdot (5^3)^{101}=25 \cdot 125^{101}. \\ \\ 11^{203}-11 \cdot 11^{202}=11 \cdot (11^2)^{101}=11 \cdot 121^{101}. \\ \\ Deoarece~32\ \textgreater \ 25~si~128^{101}\ \textgreater \ 125^{101} \Rightarrow 2^{712}\ \textgreater \ 5^{305}. \\ \\ Deoarece~25\ \textgreater \ 11~si~125^{101}\ \textgreater \ 121^{101} \Rightarrow 5^{305}\ \textgreater \ 11^{203}. \\ \\ Ordinea~crescatoare:~ \boxed{11^{203}\ \textless \ 5^{305}\ \textless \ 2^{712}}~.$