Đáp án+Giải thích các bước giải:
`1)`
`a) 2^15 . 4^13 = 2^15 . (2²)^13 = 2^15 . 2^26 = 2^(15+26) = 2^41`
`b) 25^3 . 125^5 = (5²)³ . (5³)^5 = 5^6 . 5^15 = 5^(6+15) = 5^21`
`c) 27^3 : 3^5 = (3³)³ : 3^5 = 3^9 : 3^5 = 3^(9-5) = 3^4`
`2)`
`A = 2 + 2^2 + 2^3 + ... + 2^230`
`-> 2A = 2^2 + 2^3 + 2^4 + ... + 2^230 + 2^231`
Ta có phép tính : `2A-A= (2^2 + 2^3 + 2^4 + ... + 2^230 + 2^231) - (2 + 2^2 + 2^3 + ... + 2^230)`
`-> A= (2^2 - 2^2) + (2^3 - 2^3) + (2^4-2^4) + .... + (2^230 - 2^230) - 2 + 2^231`
`-> A = 2^231 - 2`
`-> A + 2 = 2^231 - 2 + 2`
`-> A+2=2^231`
`3)`
`a) 5^36 ; 11^24`
`5^36 = 5^(3 . 12) = (5^3)^12 = 125^12`
`11^24 = 11^(2.12) = (11^2)^12 = 121^12`
Vì `125^12 > 121^12 -> 5^36 > 11^24`
`b) 3^444 ; 4^333`
`3^444 = 3^(4.111) = (3^4)^111 = 81^111`
`4^333 = 4^(3.111) = (4^3)^111 = 64^111`
Vì `81^111 > 64^111 -> 3^444 > 4^333`
`c) 128^23 < 312^18`
`d) 127^23 < 513^18`
