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Question
Simplify, giving Solution with positive index
`(1/("4ab"^2"c"))^2 div (3/(2"a"^2"bc"^2))^4`
Solution
`(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)
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