Final answer:
The coefficient of the sixth term in the binomial expansion of (a * b)^9 is 84.
Step-by-step explanation:
The binomial theorem states that for any positive integer n, the nth term in the expansion of the binomial (a + b)^n is given by:
C(n, k) * a^(n-k) * b^k
where C(n, k) represents the binomial coefficient, which is the number of ways to choose k items from a set of n items.
In this case, we have (a * b)^9, so the binomial coefficients for the terms in the expansion are:
C(9, 0) = 1, C(9, 1) = 9, C(9, 2) = 36, C(9, 3) = 84, C(9, 4) = 126, C(9, 5) = 126, C(9, 6) = 84, C(9, 6) is the coefficient of the sixth term, C(9, 7) = 36, C(9, 8) = 9, C(9, 9) = 1.
So, the coefficient of the sixth term in the binomial expansion of (a * b)^9 is 84.