Final answer:
The term independent of x in the expansion of (3x - 2/5x)¶ is found using the binomial theorem, resulting in the term -432/125.
Step-by-step explanation:
To find the term independent of x in the expansion of (3x - 2/5x)¶, we can use the binomial theorem, which allows us to expand a binomial raised to a power. In this case, the term that is independent of x will be the one where the exponents of x cancel each other out. The general term in the expansion of (a + b)^n is given by T(k+1) = C(n, k) * a^(n-k) * b^k, where C(n, k) is the binomial coefficient.
Solving for the coefficient that contains x^0, we find the term T(k+1) such that (3x)^(6-k) * (-2/5x)^k gives us x^0. This occurs when (6-k) + k = 6, as the powers of x will then cancel each other out. Thus, k must be equal to 3, and we can compute the term as C(6, 3) * (3x)^(6-3) * (-2/5x)^3.
This simplifies to 20 * 27 * (-8/125), resulting in the term -432/125 which is independent of x.