a) Ta có: \(2^{300}=\left(2^3\right)^{100}\)
\(=8^{100}\)
Ta có: \(3^{200}=\left(3^2\right)^{100}\)
\(=9^{100}\)
Ta có: \(8^{100}< 9^{100}\)
nên \(2^{300}< 3^{200}\)
b) Ta có: \(4^{30}=2^{30}\cdot2^{30}\)
\(=2^{30}\cdot\left(2^2\right)^{15}\)
\(=2^{30}\cdot4^{15}\)
Ta có: \(3\cdot24^{10}=3\cdot3^{10}\cdot8^{10}\)
\(=3^{11}\cdot8^{10}\)
\(=3^{11}\cdot2^{30}\)
Ta có: \(4^{15}>3^{15}\)
mà \(3^{15}>3^{11}\)
nên \(4^{15}>3^{11}\)
mà \(4^{30}>4^{15}\)
nên \(4^{30}>3^{11}\)
\(\Leftrightarrow2^{30}+3^{30}+4^{30}>3^{11}+3^{30}+2^{30}\)
hay \(2^{30}+3^{30}+4^{30}>3\cdot24^{10}\)
. Mk sẽ đăng từng bài 1 mog các bn giúp mk vs.... Thank you trước ạ