To simplify the expression \(-25 \cdot x^8\) over \(5 \cdot x\), we can apply the properties of exponents and simplify step by step.
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Divide the coefficients: \[ -25 \div 5 = -5 \]
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Use the property of exponents: When dividing like bases, subtract the exponents: \[ \frac{x^8}{x} = x^{8-1} = x^7 \]
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Combine the results: \[ -5 \cdot x^7 \]
Thus, the simplified expression is: \[ -5x^7 \]
So the correct option is negative 5X with a small seven.