$\\$
`( (-3)^6 . 15^5 + 9^3 . (-15)^6)/( (-3)^{10} . 5^5 . 2^3)`
`= (3^6 . (3.5)^5 + (3^2)^3 . 15^6)/(3^{10} . 5^5 . 2^3)`
`= (3^6 . 3^5 . 5^5 + 3^6 . (3.5)^6)/(3^{10} . 5^5 . 2^3)`
`= (3^6 . 3^5 . 5^5 + 3^6 . 3^6 . 5^6)/(3^{10} . 5^5 . 2^3)`
`= (3^{11} . 5^5 + 3^{12} . 5^6)/(3^{10} . 5^5 . 2^3)`
`= (3^{10} . 5^5 . (3 + 3^2 . 5) )/(3^{10} . 5^5 . 2^3)`
`= (3 + 45)/2^3`
`=6`