\(2^{91}=\left(2^{13}\right)^7=8192^7\)

\(5^{35}=\left(5^5\right)^7=3125^7\)

\(8192>3125\Rightarrow8192^7>3125^7=2^{91}>5^{35}\)

\(21^{12}=\left(21^3\right)^4=9261^4\)

\(54< 9261\Rightarrow54^4< 9261^4\Rightarrow54^4< 21^{12}\)

2^91 > 2^90

2^90=(2^5)^18=32^18

5^35<5^36

5^36=(5^2)^18=25^18

25^18<32^18

=>2^90 > 5^36

=>2^91>2^90>5^36>5^35

=>2^91>5^35

Ta có : 34¹¹ = 17¹¹.2¹¹ = 17¹¹.2048

            17¹⁴ = 17¹¹.17³ = 17¹¹.4913

Vì :2048 < 4913 

Nên : 34¹¹ < 17¹⁴ 

Ta có : 34¹¹ = 17¹¹.2¹¹ = 17¹¹.2048

            17¹⁴ = 17¹¹.17³ = 17¹¹.4913

Vì :2048 < 4913 

Nên : 34¹¹ < 17¹⁴ 

(105)^25.2  = 11025²⁵

(73)^3.25= 389017²⁵

=>107⁵⁰<73⁷⁵

Có :

\(2^{99}=2^8.2^{91}=2^8.\left(2^{13}\right)^7=2^8.8192^7\)

\(5^{35}=\left(5^5\right)^7=3125^7\)

Vì \(8192>3125\Rightarrow8192^7>3125^7\Rightarrow2^8.8192^7=3125^7\)hay \(2^{99}>3^{35}\)

a: \(2^{225}=8^{75}\)

\(3^{150}=9^{75}\)

mà 8<9

nên \(2^{225}< 3^{150}\)

b: \(2^{91}=8192^7\)

\(5^{35}=3125^7\)

mà 8192>3125

nên \(2^{91}>5^{35}\)