a) \(2^{90}\) và \(5^{30}\)
Ta có : \(2^{90}=2^{\left(3.30\right)}=\left(2^3\right)^{30}=6^{30}\)
Vì \(6^{30}>5^{30}\)
=> \(2^{90}>5^{30}\)
b) \(2^{225}\) và \(3^{150}\)
Ta có : \(2^{225}=2^{\left(3.75\right)}=\left(2^3\right)^{75}=8^{75}\)
\(3^{150}=3^{\left(2.75\right)}=\left(3^2\right)^{75}=9^{75}\)
Vì \(8^{75}< 9^{75}\)
=> \(2^{225}< 3^{150}\)
c) \(2^{200}\) và \(3^{150}\)
Ta có : \(2^{200}=2^{\left(4.50\right)}=\left(2^4\right)^{50}=16^{50}\)
\(3^{150}=3^{\left(3.50\right)}=\left(3^3\right)^{50}=27^{50}\)
Vì \(16^{50}< 27^{50}\)
=> \(2^{200}< 3^{150}\)
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 \(3^{150}\)
\(\Leftrightarrow2^{200}=\left(2^4\right)^{50};3^{150}=\left(3^3\right)^{50}\)
\(\Leftrightarrow\left(2^4\right)^{50}=16^{50};\left(3^3\right)^{50}=27^{50}\)
\(\Rightarrow16^{50}< 27^{50}\Rightarrow2^{200}< 3^{150}\)
Ta có : \(2^{90}=\left(2^3\right)^{90}=8^{30}\)
Vì \(8^{30}>5^{30}\Rightarrow2^{90}>5^{30}\)
Ta có : \(2^{225}=\left(2^3\right)^{75}=8^{75}\)
\(3^{150}=\left(3^2\right)^{75}=9^{75}\)
Vì \(9^{75}>8^{75}\) \(\Rightarrow9^{75}>8^{75}\Rightarrow2^{225}< 3^{150}\)
Ta có : \(2^{200}=\left(2^4\right)^{50}=16^{50}\)
\(3^{150}=\left(3^3\right)^{50}=27^{50}\)
VÌ \(16^{50}< 27^{50}\) \(\Rightarrow\) \(2^{200}< 3^{150}\)
C2 Vì \(2^{225}< 3^{150}\) mà \(2^{225}>2^{200}\) \(\Rightarrow\) \(3^{150}>2^{200}\)
(tính chất bắc cầu) 
