Final answer:
After simplifying the equation -1/16 ÷ (4 - 17/4)^2, we find that the answer is -1, which does not match any of the provided options. This might imply an error in the question or the options.
Step-by-step explanation:
The question asks us to solve the equation -1/16 ÷ (4 - 17/4)^2. First, we need to simplify the expression inside the parentheses: (4 - 17/4). To do this, convert the integer 4 into a fraction with a common denominator which is 16/4, then subtract 17/4 from 16/4 to get -1/4.
Next, square the result of -1/4 to get (1/4)^2, which equals 1/16. Finally, we need to divide -1/16 by 1/16. This is the same as multiplying -1/16 by the reciprocal of 1/16, which is 16/1. Thus, the answer is -1/16 × 16/1 = -1.
Therefore, the correct answer is -1, which is not listed among the options A) -16/289 B) -289/16 C) -1/289 D) 289/16, indicating a possible error in the question or the provided options. If no error is present in the question or options, an understanding might be clarified, since the mathematical process indicates a result of -1.