If f(x)=(x8)2

Question

, what is f(−4)
?(1 point)
f(−4)=

Answer 1

To evaluate \( f(-4) \) for the function \( f(x) = (x^8)^2 \):

1. Substitute \(-4\) in place of \(x\): \[ f(-4) = ((-4)^8)^2 \]

2. Calculate \((-4)^8\): \[ (-4)^8 = (4^8) \] Since raising a negative number to an even power yields a positive number.

3. Now calculate \(4^8\): \[ 4^8 = (4^4)^2 = 256^2 \] First calculate \(4^4\): \[ 4^4 = 256 \] Now calculate \(256^2\): \[ 256^2 = 65536 \] Thus, \((-4)^8 = 65536\).

4. Now, square this result: \[ f(-4) = (65536)^2 \]

5. Calculate \(65536^2\): \[ 65536^2 = 4294967296 \]

Therefore, the final value is: \[ f(-4) = 4294967296 \]