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

Question

solving for x
?(1 point)
Responses

1
1

−16
negative 16

16
16

−64

Answer 1

To solve the equation \( x^8 - 5 = -3 \), follow these steps:

1. Start with the equation: \[ x^8 - 5 = -3 \]

2. Add 5 to both sides: \[ x^8 = -3 + 5 \]

3. Simplify the right side: \[ x^8 = 2 \]

4. Now, take the eighth root of both sides: \[ x = 2^{1/8} \]

The eighth root of 2 is a positive value. None of your response options (1, -16, 16, -64) equate to \( 2^{1/8} \), so it appears there might be an error in the list of possible answers, as the correct answer isn't included. If you're looking for an approximation, \( 2^{1/8} \) is approximately 1.0905.