Explanation:

To solve the expression [(256)^-2] raised to the power 1/4, we need to follow a step-by-step process. Let's break it down:

Step 1: Evaluate the expression inside the square brackets.
- [(256)^-2] = 1/(256^2)
- 256^2 = 256 * 256 = 65,536
- Therefore, 1/(256^2) = 1/65,536

Step 2: Simplify the expression obtained in Step 1.
- 1/65,536 raised to the power 1/4 = (1/65,536)^(1/4)

Step 3: Simplify the expression further using the exponent rule.
- (a^m)^n = a^(m*n)
- In this case, a = 1/65,536, m = 1/4, and n = 4
- (1/65,536)^(1/4) = 1/65,536 * 1/4 = 1/256

Step 4: Finalize the answer.
- The expression [(256)^-2] raised to the power 1/4 simplifies to 1/256.

Summary:

After evaluating the expression [(256)^-2] raised to the power 1/4, we found that the final answer is 1/256.