`a,3^2 .1/243 .81^2 .1/3^3`

`= 3^2 . 1/3^5 . 3^8 . 1/3^3`

`= 1/3^3 . 1/3^3 . 3^8`

`= 1/3^6 . 3^8 = 3^2 = 9`

`b,(4.2^5 ):(2^3 .1/16)`

`=(2^2 . 2^5) : (2^3 . 1/2^4)`

`=2^7 : 1/2 = 2^8`

`c,(2^-1+3^-1):(2^-1-3^-1)+(2^-1 .2^0):2^3`

`= (1/2 + 1/3): ( 1/2 - 1/3) + ( 1/2 . 1) : 2^3`

`= 5/6 : 1/6 + 1/2^4`

`= 5 + 1/16 = 5 1/16`

`d,(-1/3)^-1 -(-6/7)^0+(1/2)^2 : 2`

`= -3 - 1 + 1/4 . 1/2` 

`= -4 + 1/8 = -31/8`