\(199^{20}\)\(< \)\(200^{20}\)\(=\)\(\left(2^3.5^2\right)^{20}\)\(=\)\(2^{60}\)\(.\)\(5^{40}\)
\(2003^{15}\)\(>\)\(2000^{15}\)\(=\)\(\left(2^4.5^3\right)^{15}\)\(=\)\(2^{60}\)\(.\)\(5^{45}\)
\(\Rightarrow\)\(2^{60}\)\(.\)\(5^{40}\)\(< \)\(2^{60}\)\(.\)\(5^{45}\)
\(\Rightarrow\)...........................................
199^20 = (199^4) ^5
2003^15 = (2003^3)^5
Vì 199^4 < 2003^3 => 199^20 < 2003^15
Có: \(199^{20}=199^{4.5}=\left(199^4\right)^5=1568239201^5\)
\(2003^{15}=2003^{3.5}=\left(2003^3\right)^5=8036054027^5\)
Có : 8036054027 > 1568239201
=> \(199^{20}< 2003^{15}\)
Ủng hộ mik nhá ^_^"
\(199^{20}< 200^{20}=\left(2^3\cdot5^2\right)^{20}=2^{60}\cdot5^{40}\)
\(2003^{15}>2000^{15}=\left(2\cdot10^3\right)^{15}=\left(2^4\cdot5^3\right)^{15}=2^{60}\cdot5^{45}\)
\(\Leftrightarrow2^{60}\cdot5^{40}< 2^{60}\cdot5^{45}\)
\(\Rightarrow199^{20}< 2003^{15}\)
