Question

What is the value of the expression \(4(2y)^{2y-x}\) when \(x = 2\) and \(y = 4\)?

a) \(4\)
b) \(8/3\)
c) \(125\)
d) \(12/5\)
e) I don't know.

Answer 1

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.