Final answer:
The expression 4(2y)^{2y-x} evaluates to 1,048,576 when x = 2 and y = 4, which doesn't match any of the provided options (a) 4, (b) 8/3, (c) 125, (d) 12/5, or (e) I don't know.
Step-by-step explanation:
The question asks us to evaluate the expression 4(2y)^{2y-x} when x = 2 and y = 4. First, plug in the given values for x and y into the expression:
4(2×4)^{2×4-2} = 4(8)^{8-2} = 4(8)^6.
Next, calculate the power of 8:
8^6 = 262,144.
After calculating the power, multiply by 4:
4 × 262,144 = 1,048,576.
So, the value of the expression when x = 2 and y = 4 is 1,048,576, which is not one of the options provided (a through e). This suggests there might be a mistake in the provided options or that none of the options correctly represent the value of the expression.