To solve the equation \( x^8 = -8 \), we first note that the left side, \( x^8 \), represents the eighth power of \( x \). Since powers of real numbers (especially even powers, like 8) are always non-negative, \( x^8 \) cannot equal a negative number like -8.
Thus, there are no real solutions to the equation \( x^8 = -8 \).
So if you were to consider the responses provided:
- \( x = 64 \)
- \( x = 0 \)
- \( x = -64 \)
- \( x = -1 \)
None of these responses are correct since \( x^8 \) cannot equal -8. The equation has no real solutions.
If you are asked for complex solutions, you may find them by taking the complex eighth root of -8, but in the context of real numbers, the answer is that there are no solutions.