Question

Simplify, giving Solution with positive index

`(1/("4ab"^2"c"))^2 div (3/(2"a"^2"bc"^2))^4`

Answer 1

`(1/("4ab"^2"c"))^2 div (3/(2"a"^2"bc"^2))^4`

`= (1/"4ab"^2"c")^2 xx ((2"a"^2"bc"^2)/3)^4`

`= 1^2/(4^2"a"^2"b"^(2xx2) ."c"^2) xx (2^4 "a"^(2xx4) . "b"^4 . "c"^(2xx4))/3^4`

`= 1^2/3^4 xx "a"^(8-2) "b"^(4 - 4) "c"^(8-2)`   (∵ 2⁴ = 4²)

`= 1/(3 xx 3 xx 3 xx 3) "a"^6"b"^0"c"^6`

`= 1/81 "a"^6"c"^6`   (∵ b⁰ = 1)