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Question
Simplify the following:
`((36"m"^-4)/(49"n"^-2))^(-3/2)`
Solution
`((36"m"^-4)/(49"n"^-2))^(-3/2)`
= `((6^2"m"^-4)/(7^2"n"^-2))^(-3/2)`
= `((6^(2xx(-3/2))"m"^(-4xx (-3/2)))/(7^(2xx(-3/2))"n"^-2xx(-3/2))) .......("Using" ("a" xx "b")^"n" = "a"^"n" xx "b"^"n" and ("a"/"b")^"n" = "a"^"n"/"b"^"n")`
= `(6^-3"m"^6)/(7^-3"n"^3)`
= `(7^3"m"^6)/(6^3"n"^3) ......("Using" "a"^-"n" = 1/"a"^"n")`
= `(343"m"^6)/(216"n"^3)`.
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