\(119^{20}=\)324294234694341316421188266002423799213601
\(2017^{15}=\)37203900413164153009430455381866296090367077685793
=>119^20<2017^15
Mình có cách rồi
\(238^{15}< 2017^{15}\)
\(238^{15}=119^{15}\cdot2^{15}=238^{10}\cdot238^5\)
\(=\left(119^{10}\cdot2^{10}\right)\cdot\left(119^5\cdot2^5\right)\)
\(=119^{10}\cdot119^5\cdot2^{10}\cdot2^5\)
\(=119^{10}\cdot238^5\cdot2^{10}\)
\(=119^{10}\cdot238^5\cdot2^5\cdot2^5=119^{10}\cdot238^5\cdot2^5\cdot2^5=119^{10}\cdot476^5\cdot2^5\)
\(119^{20}=119^{10}\cdot119^{10}\)
Ta có :\(119^{10}< 476^5\cdot2^5\)
\(\Rightarrow119^{10}\cdot119^{10}< 119^{10}\cdot476^5\cdot2^5\)
\(\Rightarrow119^{20}< 2017^{15}\)
