Question

Solve for x.
x8=−8(1 point)
Responses

x=64
x equals 64

x=0
x equals 0

x=−64
x equals negative 64

x=−1
x equals negative 1
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Answer 1

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.