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
therer are no errors the answer is on this list

Answer 1

To solve the equation \( x^8 - 5 = -3 \), we can start by adding 5 to both sides of the equation:

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

This simplifies to:

\[ x^8 = 2 \]

Now, to solve for \( x \), we take the eighth root of both sides:

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

The numerical approximation of \( \sqrt[8]{2} \) is a positive number, approximately equal to \( 1.0905 \).

Given the available choices:

1. \( 1 \)
2. \( -16 \)
3. \( 16 \)
4. \( -64 \)

None of these options are correct, as \( \sqrt[8]{2} \) is not equal to any of those values. The answer lies outside the provided options. Therefore, the correct answer is that there are no errors; the answer is not on this list.