giúp em từ câu 6 đến 10 với ạ
6: \(3^{2n}=\left(3^2\right)^n=9^n;2^{3n}=\left(2^3\right)^n=8^n\)
mà 9>8
nên \(3^{2n}>2^{3n}\)
7: \(199^{20}< 200^{20}=\left(2^3\cdot5^2\right)^{20}=2^{60}\cdot5^{40}\)
\(2003^{15}>2000^{15}=\left(2\cdot10^3\right)^{15}=\left(2^4\cdot5^3\right)^{15}=2^{60}\cdot5^{45}\)
mà \(5^{45}>5^{40}\)
nên \(2003^{15}>199^{20}\)
8: \(3^{30}=\left(3^{10}\right)^3;11^{21}=\left(11^7\right)^3\)
mà \(3^{10}< 11^7\)
nên \(3^{30}< 11^{21}\)
9: \(72^{45}-72^{44}=72^{44}\left(72-1\right)=72^{44}\cdot71\)
\(72^{44}-72^{43}=72^{43}\left(72-1\right)=72^{43}\cdot71\)
mà 44>43
nên \(72^{45}-72^{44}>72^{44}-72^{43}\)
10: \(2^7=128;7^2=49\)
mà 128>49
nên \(2^7>7^2\)
