Introduction:
The maximum number of prime implicants for an n-variable Boolean function can be determined by analyzing the number of possible minterms and their combinations. Each minterm can be represented as a product term, and a prime implicant is a product term that cannot be further minimized. Therefore, the number of prime implicants will depend on the number of minterms and their combinations.

Explanation:
To find the maximum number of prime implicants for an n-variable Boolean function, we need to consider the worst-case scenario, where every minterm is a separate prime implicant. In this case, each minterm will correspond to a unique product term that cannot be further minimized.

Step 1: Determine the number of minterms:
The number of minterms in an n-variable Boolean function can be calculated using the formula 2^n. This is because each variable can take on two possible values (0 or 1), and there are n variables in total.

Step 2: Calculate the number of combinations:
For each minterm, we can choose to include it in a prime implicant or exclude it. Therefore, there are 2 possibilities for each minterm. Since there are 2^n minterms, the total number of combinations will be 2^(2^n).

Step 3: Determine the maximum number of prime implicants:
In the worst-case scenario, each combination corresponds to a separate prime implicant. Therefore, the maximum number of prime implicants is equal to the number of combinations, which is 2^(2^n).

Conclusion:
In conclusion, the maximum number of prime implicants for an n-variable Boolean function is 2^(2^n). This means that as the number of variables increases, the number of possible prime implicants grows exponentially. Therefore, option 'D' - 2(n-1) is the correct answer.