`a)`
`2023^0 + (-9)/16 . 13/27 + 9/16 . (-14)/27`
`= 1 + (-9)/16 . 13/27 + (-9)/16 . 14/27`
`= 1 + (-9)/16 . (13/27 + 14/27)`
` = 1 + (-9)/16 . 1`
`= 1 - 9/16`
`= 7/16`
`b)`
`(2/3)^2 . (-1 2/3) - 5/9 . 4/3 + (-5)/3 . (-1/3)^2`
` = 4/9 . (-5)/3 - 5/9 . 4/3 + (-5)/3 . 1/9`
` = (4/9 . (-5)/3 + (-5)/3 . 1/9 ) - 5/9 .4/3`
`= (-5)/3 . (4/9 + 1/9) - 5/9 . 4/3`
`= (-5)/3 . 5/9 - 5/9 . 4/3`
`= 5/9 . ( (-5)/3 - 4/3)`
`= 5/9 . (-3)`
` = (-5)/3`
`c)`
`7/18 . ( (-12)/23 - 4/15) + 7/18 . (8/30 + 35/23)`
` = 7/18 . ( (-12)/23- 4/15 + 8/30 + 35/23)`
` = 7/18 . [ ((-12)/23 + 35/23) + (8/30 - 4/15)]`
`= 7/18 . (1+0)`
` = 7/18 . 1`
` = 7/18`
