What is the solution to the equation x8 − 5 = −3

Question

solving for x
?(1 point)

−64
negative 64 -

1
1 - no response given

−16
negative 16 - no response given

16

Answer 1

To solve the equation \( x^8 - 5 = -3 \), we can start by isolating \( x^8 \).

1. Add 5 to both sides of the equation:

   \[ x^8 - 5 + 5 = -3 + 5 \]

   This simplifies to:

   \[ x^8 = 2 \]

2. Now we take the eighth root of both sides:

   \[ x = \pm \sqrt[8]{2} \]

Since \( \sqrt[8]{2} \) is a positive value, the potential solutions are positive and negative eighth roots. However, none of the options given (-64, 1, -16, 16) are solutions to the equation \( x^8 = 2 \).

Therefore, the final answer is not among the choices provided.