`\color{#fc1100}{♡}\color{#ff483b}{T}\color{#ff655a}{u}\color{#ff857c}{ấ}\color{#feb8b3}{n}`

`bb(d.)`

`(10^2 + 11^2 + 12^2) : (13^2 + 14^2)`

`= (100 + 121 + 144) : (169 + 196)`

`= 365 : 365`

`= 1`

`bb(e.)`

`(2^3 . 9^4 + 9^3 . 45) : (9^2 . 10 + 9^2 . 3)`

`= (2^3 . 9^4 + 9^3 . 9 . 5) : (9^2 . (10 + 3))`

`= (2^3 . 9^4 + 9^4 . 5) : (9^2 . 13)`

`= (9^4 . (2^3 + 5)) : (9^2 . 13)`

`= (9^4 . (8 + 5)) : (9^2 . 13)`

`= (9^4 . 13) : (9^2 . 13)`

`= 9^4 / 9^2`

`= 9^2`

`= 81`

`bb(g.)`

`(4^6 . 9^5 + 6^9 . 120) / (8^4 . 3^12 - 6^11)`

`= ((2^2)^6 . (3^2)^5 + (2 . 3)^9 . 2^3 . 3 . 5) / ((2^3)^4 . 3^12 - (2 . 3)^11)`

`= (2^12 . 3^10 + 2^9 . 3^9 . 2^3 . 3 . 5) / (2^12 . 3^12 - 2^11 . 3^11)`

`= (2^12 . 3^10 + 2^12 . 3^10 . 5) / (2^11 . 3^11 . (2 . 3 - 1))`

`= (2^12 . 3^10 . (1 + 5)) / (2^11 . 3^11 . (6 - 1))`

`= (2^12 . 3^10 . 6) / (2^11 . 3^11 . 5)`

`= (2^12 . 3^10 . 2 . 3) / (2^11 . 3^11 . 5)`

`= (2^13 . 3^11) / (2^11 . 3^11 . 5)`

`= 2^2 / 5`

`= 4/5`

`bb(h.)`

`(9 . 5^20 . 27^9 - 3 . 9^15 . 25^9) / (7 . 3^29 . 125^6 - 3 . 3^9 . 15^19)`

`= (3^2 . 5^20 . (3^3)^9 - 3 . (3^2)^15 . (5^2)^9) / (7 . 3^29 . (5^3)^6 - 3^10 . (3 . 5)^19)`

`= (3^2 . 5^20 . 3^27 - 3 . 3^30 . 5^18) / (7 . 3^29 . 5^18 - 3^10 . 3^19 . 5^19)`

`= (3^29 . 5^20 - 3^31 . 5^18) / (7 . 3^29 . 5^18 - 3^29 . 5^19)`

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

`= (25 - 9) / (7 - 5)`

`= 16 / 2`

`= 8`

`bb(i.)`

`(5^2 . 6^11 . 16^2 + 6^2 . 12^6 . 15^2) / (2 . 6^12 . 10^4 - 81^2 . 960^3)`

`= (5^2 . (2 . 3)^11 . (2^4)^2 + (2 . 3)^2 . (2^2 . 3)^6 . (3 . 5)^2) / (2 . (2 . 3)^12 . (2 . 5)^4 - (3^4)^2 . (2^6 . 3 . 5)^3)`

`= (5^2 . 2^11 . 3^11 . 2^8 + 2^2 . 3^2 . 2^12 . 3^6 . 3^2 . 5^2) / (2 . 2^12 . 3^12 . 2^4 . 5^4 - 3^8 . 2^18 . 3^3 . 5^3)`

`= (2^19 . 3^11 . 5^2 + 2^14 . 3^10 . 5^2) / (2^17 . 3^12 . 5^4 - 2^18 . 3^11 . 5^3)`

`= (2^14 . 3^10 . 5^2 . (2^5 . 3 + 1)) / (2^17 . 3^11 . 5^3 . (3 . 5 - 2))`

`= (2^14 . 3^10 . 5^2 . (32 . 3 + 1)) / (2^17 . 3^11 . 5^3 . (15 - 2))`

`= (2^14 . 3^10 . 5^2 . 97) / (2^17 . 3^11 . 5^3 . 13)`

`= 97 / (2^3 . 3 . 5 . 13)`

`= 97 / (8 . 3 . 5 . 13)`

`= 97 / 1560`

`bb(k.)`

`(7 . 6^10 . 2^10 . 3^6 - 2^19 . 6^15) / (9 . 6^19 . 2^9 - 4 . 3^17 . 2^26)`

`= (7 . (2 . 3)^10 . 2^10 . 3^6 - 2^19 . (2 . 3)^15) / (3^2 . (2 . 3)^19 . 2^9 - 2^2 . 3^17 . 2^26)`

`= (7 . 2^10 . 3^10 . 2^10 . 3^6 - 2^19 . 2^15 . 3^15) / (3^2 . 2^19 . 3^19 . 2^9 - 2^28 . 3^17)`

`= (7 . 2^20 . 3^16 - 2^34 . 3^15) / (2^28 . 3^21 - 2^28 . 3^17)`

`= (2^20 . 3^15 . (7 . 3 - 2^14)) / (2^28 . 3^17 . (3^4 - 1))`

`= (21 - 16384) / (2^8 . 3^2 . (81 - 1))`

`= -16363 / (256 . 9 . 80)`

`= -16363 / 184320 .`