Bài `1`

`1)`

`A=(45^3·20^4·18^2)/(180^5)`

`A=((3^2·5)^3·(2^2·5)^4·(2·3^2)^2)/((2^2·3^2·5)^5)`

`A=(3^6·5^3·2^8·5^4·2^2·3^4)/(2^10·3^10·5^5)`

`A=(2^10·3^10·5^7)/(2^10·3^10·5^5)`

`A=5^2`

`A=25`

`2)`

`B=(8·9^3+2^7·9^2)/(5^2·6^3)`

`B=(2^3·(3^2)^3+2^7·(3^2)^2)/(5^2·(2·3)^3)`

`B=(2^3·3^6+2^7·3^4)/(5^2·2^3·3^3)`

`B=(2^3·3^4·(3^2+2^4))/(5^2·2^3·3^3)`

`B=3(3^2+2^4)/(5^2)`

`B=(3(9+16))/(5^2)`

`B=(3·25)/25`

`B=3`

`C=3^50+3^49+3^48+...+3^2+3`

`3C=3(3^50+3^49+3^48+...+3^2+3)`

`3C=3^51+3^50+3^49+...+3^3+3^2`

`3C-C=3^51+3^50+3^49+...+3^3+3^2-(3^50+3^49+3^48+...+3^2+3)`

`2C=3^51-3`

`C=(3^51-3)/2`

`4)`

`B=(72^3·54^3÷8^3)/(108^5÷4^5)`

`B=((72·54÷8)^3)/((108÷4)^5)`

`B=(468^3)/(27^5)`

`B=((2·3^5)^3)/((3^3)^5)`

`B=(2^3·3^15)/(3^15)`

`B=2^3`

`B=8`

Bài `2`

`A=3+3^2+3^3+...+3^100`

`3A=3(3+3^2+3^3+...+3^100)`

`3A=3^2+3^3+3^4+...+3^101`

`3A-A=3^2+3^3+3^4+...+3^101-(3+3^2+3^3+...+3^100)`

`2A=3^101-3`

`A=(3^101-3)/2`

Ta có: `2A+3=2·(3^101-3)/2+3=3^101-3+3=3^101`

Mà `3^101` là một luỹ thừa của `3`

Vậy `2A+3` là một luỹ thừa của `3`