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

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

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

`= (5 . 2^30 . 3^18 - 2^29 . 3^20)/(5 . 2^28 . 3^19 - 7 . 2^29 . 3^18)` 

`= (2^29 . 3^18 . (5 . 2 - 3^2))/(2^28 . 3^18 . (5 . 3 - 7 . 2))` 

`= (2 . (10 - 9))/(15 - 14)` 

`= (2 . 1)/1` 

`= 2`