What is the largest number among the following?

Correct Option: (a) (1/2)^(-6)

Let us evaluate each option by simplifying the exponents: (a) (1/2)^(-6) = ((1/2)^(-1))^6 = 2^6 = 64. (b) (1/4)^(-3) = ((1/4)^(-1))^3 = 4^3 = 64. (c) (1/3)^(-4) = ((1/3)^(-1))^4 = 3^4 = 81. (d) (1/6)^(-2) = ((1/6)^(-1))^2 = 6^2 = 36. Comparing the calculated values: 64, 64, 81, and 36. The largest number among them is 81, which corresponds to option (c). Wait! Let me re-read option (c): (1/3)^(-4) = 81. Let me check if option (c) is indeed the largest. Yes, 81 is greater than 64, 64, and 36. Therefore, option (c) is the largest number. Wait, let me check the option index for (1/3)^(-4). In the options list: (a) (1/2)^(-6), (b) (1/4)^(-3), (c) (1/3)^(-4), (d) (1/6)^(-2). Since index is 0-based, (c) is at index 2. Therefore, correct_option_index is 2.