`(5.4^(15).9^9-4.3^(20).8^9)/(5.2^(9).6^(19)-7.2^(29).27^(6))`

`= (5.(4^15).(9^9) - 4.(3^20).(8^9))/(5.(2^9).(6^19) - 7.(2^29).(27^6))`

`= (5.(2^30).(3^18) - 4.(3^20).(2^27))/(5.(2^9).(2^19).(3^19) - 7.(2^29).(3^18))`

`= (5.2^(30).3^(18) - 4.3^(20).2^27)/(5.2^(28).3^19 - 7.2^(29).3^18)`

`= [2^(27).3^(18).(5.2^3 - 4.3^2)]/[2^(28).3^(18).(5.3- 7.2)]`

`= [2^(27).3^(18).(40 - 36)]/[2^(28).3^(18).(15 - 14)]`

`= [2^(27).3^(18).4]/[2^(28).3^(18).1]`

`= (4)/(2)`

`= 2`

`@` ltmn