`a)`
`(-3/4)^4 : (-9/8)^4`
`= [-3/4 : (-9/8)]^4`
`= (2/3)^4`
`= 16/81`
`b)`
`(7/8)^5 : (21/16)^5`
`= (7/8 : 21/16)^5`
`= (2/3)^5`
`= 32/243`
`c)`
`(1/9)^2012 : (1/8)^2012`
`= (1/9 : 1/8)^2012`
`= (8/9)^2012`
`= (8^2012)/(9^2012)`
`d)`
`(-3/4)^5 . (16/9)^5`
`= (-3/4 . 16/9)^5`
`= (-4/3)^5`
`= -1024/243`
`e)`
`(1/3)^4 . ((-9)/2)^6`
`= [(1/3)^2]^2 . [((-9)/2)^3]^2`
`= (1/9)^2 . (-729/8)^2`
`= [1/9 . (-729/8)]^2`
`= (-81/8)^2`
`= 6561/64`
`g)`
`(-31/8)^3 . (-32/31)^4`
`= -(31^3)/(8^3) . (32^4)/(31^4)`
`= -(31^3 . 32^4)/(8^3 . 31^4)`
`= -(31^3 . 2^20)/(2^9 . 31^4)`
`= -(2^11)/31`
`= -2048/31`
