Đáp án+Giải thích các bước giải:

 Bài `2:`

`a)` Ta có: `2^{100}=(2^{5})^{20}=32^{20}`

`5^{40}=(5^{2})^{20}=25^{20}`

Mà `32>25`

Nên: `32^{20}>25^{20}`

Hay: `2^{100}> 5^{40}`

Vậy `2^{100}>5^{40}`

`b)` Ta có: `6.5^{22}` ta giữ nguyên

`5^{23}=5^{22+1}=5^{22}.5^{1}=5^{22}.5`

Ta có: `5<6`

Nên: `5.5^{22}<6.5^{22}`

Hay: `5^{23}< 6.5^{22}`

Vậy `5^{23}<6.5^{22}`

`c)` Ta có: `7.2^{13}` ta giữ nguyên

`2^{16}=2^{13+3}=2^{13}.2^{3}=2^{13}.8`

Do `7<8`

Nên: `7. 2^{13}< 2^{13}.8`

Hay: `7.2^{13}<2^{16}`

Vậy `7.2^{13}<2^{16}`

`e)` Ta có: `21^{15}` ta giữ nguyên

`27^{5}.49^{8}=(3^{3})^{5}.(7^{2})^{8}`

`=3^{15}.7^{16}`

`=3^{15}.7^{15+1}`

`=3^{15}.7^{15}.7`

`=(3.7)^{15}.7`

`=21^{15}.7`

Mà `21^{15}=21^{15}`

Do đó: `21^{15}< 21^{15}.7`

Hay: `21^{15}< 27^{5}.49^{8}`

Vậy `21^{15}<27^{5}.49^{8}`

`d)` Ta có: `2^{45}=(2^{3})^{15}=8^{15}`

`3^{30}=(3^{2})^{15}=9^{15}`

Do `8<9`

Nên: `8^{15}<9^{15}`

Hay: `2^{45}< 3^{30}`

Vậy `2^{45}<3^{30}`

`f)` Ta có: `625^{55}=(5^{4})^{55}=5^{4.55}=5^{220}`

`125^{73}=(5^{3})^{73}=5^{3.73}=5^{219}`

Ta xét số mũ nhận thấy: `220>219`

Nên: `5^{220}> 5^{219}`

Hay: `625^{55}> 125^{73}`

Vậy `625^{55}>125^{73}`

`g)` Ta có: `2^{210}=(2^{7})^{30}=128^{30}`

`5^{90}=(5^{3})^{30}=125^{30}`

Do `128>125`

Nên: `128^{30}> 125^{30}`

Hay: `2^{210}> 5^{90}`

Vậy `2^{210}>5^{90}`

`h)` Ta có: `27^{50}=(3^{3})^{50}=3^{3.50}=3^{150}`

`81^{38}=(3^{4})^{38}=3^{4.38}=3^{152}`

Ta xét số mũ nhận thấy: `150<152`

Nên: `3^{150}<3^{152}`

Hay: `27^{50}< 81^{38}`

Vậy `27^{50}<81^{38}`