Solve for x . x8=−8 (1 point) Responses x=64 x equals 64 x=−1 x equals negative 1 x=−64 x equals negative 64 x=0 x equals 0

Answer 1

To solve the equation \( x^8 = -8 \), we can analyze the left and right sides of the equation.

The left side, \( x^8 \), represents a real number because raising a real number to an even power (in this case, 8) will always yield a non-negative result. Therefore, \( x^8 \) will always be 0 or a positive number.

The right side, \(-8\), is a negative number.

Since there is no real number \( x \) such that \( x^8 \) can equal a negative number, the equation \( x^8 = -8 \) has no real solutions.

Thus, none of the provided responses (64, -1, -64, or 0) are correct.

The solution is that there are no real solutions for \( x^8 = -8 \).