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Question
Simplify:
`(4/13)^4 xx (13/7)^2 xx (7/4)^3`
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Solution
Given, `(4/13)^4 xx (13/7)^2 xx (7/4)^3`
= `(4)^4/(13)^4 xx (13)^2/(7)^2 xx (7)^3/(4)^3`
= `(4)^4 xx (4)^-3 xx (13)^2 xx (13)^-4 xx (7)^3 xx (7)^-2` ...`[∵ a^-m = 1/a^m]`
= `(4)^(4 - 3) xx (13)^(2 - 4) xx (7)^(3 - 2)` ...`[∵ a^m xx a^n = a^(m - n)]`
= `(4)^1 xx (13)^-2 xx (7)^1`
= `4 xx 1/169 xx 7` ...`[∵ a^-m = 1/a^m]`
= `28/169`
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