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The coefficient of a^(-6) b^(4) in the e...

The coefficient of `a^(-6) b^(4)` in the expansion of `((1)/(a) - (2b)/(3))^(10)` is......

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Given expansion is `((1)/(a) - (2b)/(3))^(10)`
Let `T_(r + 1)` has the coefficient of `a^(-6) b^(4)`
`:. T_(r + 1) = .^(10)C_(r) ((1)/(a))^(10 - r) (-(2b)/(3))^(r)`
For coefficient of `a^(-6) b^(4), " " 10 - r = 6 rArr r = 4`
Coefficient of `a^(-6) b^(4) = .^(10)C_(4) (-2//3)^(4)`
`:. = (10.9.8.76!)/(6!.4.3.2.1).(2^(4))/(3^(4)) = (1120)/(27)`
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