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

Explanation

To find the coefficient of \( a^{-6} b^{4} \) in the expansion of \( \left( \frac{1}{a} - \frac{2b}{3} \right)^{10} \), we can use the Binomial Theorem, which states that:

\[ (x + y)^n = \sum_{r=0}^{n} \binom{n}{r} x^{n-r} y^r \]

In our case, we can identify \( x = \frac{1}{a} \) and \( y = -\frac{2b}{3} \), and we need to expand \( \left( \frac{1}{a} - \frac{2b}{3} \right)^{10} \).

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