`a)2^{300}=(2^3)^100=8^100`

`3^200=(3^2)^100=9^100`

Vì `9^100>8^100`

`=>2^300<3^200`

`b)3xx24^10`

`=3.(3.8)^10`

`=3^{11}.8^10`

`=3^{11}.2^30`

`2^300=2^{30}.2^{270}`

`=2^{30}.8^{90}`

Vì `3^11<8^90`

`=>3^{11}.2^30<8^{90}.2^30=2^300`

`=>3xx24^{10}<2^300+3^20+4^30`

Ta có: \(4^{30}=2^{30}.2^{30}=\left(2^3\right)^{10}.\left(2^2\right)^{15}=8^{10}.4^{15}>8^{10}.3^{15}>8^{10}.3^{11}\) (1)

Mà  \(8^{10}.3^{11}=8^{10}.3^{10}.3=\left(8.3\right)^{10}.3=24^{10}.3\)  (2)

Từ (1);(2)=> \(4^{30}>3.24^{10}\)

Vậy \(2^{30}+3^{30}+4^{30}>3.24^{10}\)

ta có 4³⁰=2³⁰.2³⁰=(2³)¹⁰.(2²)¹⁵=8¹⁰.4¹⁵

mà 8¹⁰.4¹⁵>8¹⁰.3¹⁵\(\Rightarrow\) 8¹⁰.4¹⁵>8¹⁰.3¹¹

mặt khác 8¹⁰ .3¹¹=8¹⁰.3¹⁰.3=24¹⁰ .3 \(\Rightarrow\) 4³⁰>24¹⁰.3

ta lại có 2³⁰>0 , 3³⁰>0 nên 2³⁰+3³⁰+4³⁰>4³⁰

\(\Rightarrow\) 2³⁰+3³⁰+4³⁰>4³⁰>3.24¹⁰

\(\Rightarrow\) 2³⁰+3³⁰+4³⁰>3.24¹⁰

vậy 2³⁰+3³⁰+4³⁰>3.24¹⁰