To solve the equation \( x^8 - 5 = -3 \), we first isolate \( x^8 \):
\[ x^8 - 5 = -3 \]
Add 5 to both sides:
\[ x^8 = -3 + 5 \]
\[ x^8 = 2 \]
Next, we take the eighth root of both sides to find \( x \):
\[ x = \pm \sqrt[8]{2} \]
The eighth root of 2 is a positive number, so we can express the two possible solutions as:
\[ x = \sqrt[8]{2} \quad \text{and} \quad x = -\sqrt[8]{2} \]
However, none of the responses provided (16, -16, -64, 1, -64) match \(\pm \sqrt[8]{2}\). Therefore, none of the given options are correct solutions for the equation.
If you’re looking for a numerical approximation:
\[ \sqrt[8]{2} \approx 1.0905 \]
As a summary, the solutions to the equation do not correspond to any of the responses you listed.
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