`a, (2^15 . 3^6 . 7)/(9^3 . 8^5 . 21)`
`= (2^15 . 3^6 . 7)/((3^2)^3 . (2^3)^5 . 3 . 7)`
`= (2^15 . 3^6 . 7)/(3^6 . 2^15 . 3 . 7)`
`= 1/3`
`b, (100^2)/(2^4)`
`= (100 . 100)/(2^4)`
`= (2 . 2 . 25 . 2 . 2 . 25)/(2^4)`
`= (2^4 . 25 . 25)/(2^4)`
`= 25 . 25 = 625`
`c, (45^10 . 5^20)/(75^15)`
`= ((3 . 15)^10 . 5^20)/((15 . 5)^15)`
`= (15^10 . 3^10 . 5^20)/(15^15 . 5^15)`
`= (15^10 . 3^10 . 5^15 . 5^5)/(15^10 . 15^5 . 5^15)`
`= (3^10 . 5^5)/(15^5)`
`= (3^10 . 5^5)/((3 . 5)^5)`
`= (3^10 . 5^5)/(3^5 . 5^5)`
`= (3^10)/(3^5)`
`= (3^5 . 3^5)/(3^5)`
`= 3^5 = 243`
