Đáp án+Giải thích các bước giải:

`a)` `\text{Ta có:` `2^300 = (2^3)^100 = 8^100`

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

`\text{Vì 8 < 9 nên` `8^100 < 9^100.`

`\text{Vậy` `2^300 < 3^200.`

`b)` `\text{Ta có:` `3^500 = (3^5)^100 = 243^100`

`7^300 = (7^3)^100 = 343^100`

`\text{Vì 243 < 343 nên` `243^100 < 343^100.`

`\text{Vậy` `3^500 < 7^300.`

`c)` `8^5 = (2^3)^5 = 2^15`

`4^7 = (2^2)^7 = 2^14`

`3*4^7 = 3 * 2^14`

`\text{Vì 2 < 3 nên` `2*2^14 < 3*2^14.`

`\text{Vậy` `8^5 < 3*4^7.`

`e)` `9999^10 = (99*101)^10 = 99^10 * 101^10`

`99^20 = 99^10 * 99^10`

`\text{Vì` `99^10 < 101^10` `\text{nên` `99^10 * 99^10 < 99^10 * 101^10.`

`\text{Vậy` `99^20 < 9999^10.`

`f) `\text{Ta có:` `11^1979 < 11^1980 = (11^3)^660 = 1331^660`

`37^1320 = (37^2)^660 = 1369^660`

`\text{Vì 1331 < 1369 nên` `11^1979 < 37^1320.`

`g)` `\text{Ta có:` `10^10 = (10^2)^5 = 100^5`

`48*50^5`

`100^5 = (2*50)^5 = 2^5 * 50^5 = 32 * 50^5`

`\text{Vì 32 < 48 nên` `32 * 50^5 < 48 * 50^5.`

`\text{Vậy` `10^10 < 48*50^5.`

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