a,\(2^{90}\) và \(5^{30}\)
\(\Leftrightarrow2^{90}=\left(2^3\right)^{30}\);\(5^{30}=\left(5^1\right)^{30}\)
\(\Leftrightarrow\left(2^3\right)^{30}=8^{30};\left(5^1\right)^{30}=5^{30}\)
\(\Rightarrow8^{30}>5^{30}\Rightarrow2^{90}>5^{30}\)
b,\(2^{225}\) và \(3^{150}\)
\(\Leftrightarrow2^{225}=\left(2^3\right)^{75};3^{150}=\left(3^2\right)^{75}\)
\(\Leftrightarrow\left(2^3\right)^{75}=8^{75};\left(3^2\right)^{75}=9^{75}\)
\(\Rightarrow8^{75}< 9^{75}\Rightarrow2^{225}< 3^{150}\)
c,\(2^{200}\) và \(3^{150}\)
\(\Leftrightarrow2^{200}=\left(2^4\right)^{50};3^{150}=\left(3^3\right)^{50}\)
\(\Leftrightarrow\left(2^4\right)^{50}=16^{50};\left(3^3\right)^{50}=27^{50}\)
\(\Rightarrow16^{50}< 27^{50}\Rightarrow2^{200}< 3^{150}\)
