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Question
Simplify the following:
`((64"a"^12)/(27"b"^6))^(-2/3)`
Solution
`((64"a"^12)/(27"b"^6))^(-2/3)`
= `((2^6 "a"^12)/(3^3"b"^6))^(-2/3)`
= `((2^(6xx(-2/3)) "a"^(12xx(-2/3)))/(3^(3xx^((-2/3)))"b"^(6xx(-2/3)))) ......("Using"("a" xx "b"^"n") = "a"^"n" xx "b"^"n" and ("a"/"b")^"n" = "a"^"n"/"b"^"n")`
= `(2^-4 "a"^-8)/(3^-2"b"^-4)`
= `(3^2"b"^4)/(2^4"a"^8) .....("Using" "a"^-"n" = 1/"a"^"n")`
= `(9"b"^4)/(16"a"^8)`.
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