To simplify the expression \(-25x^8 / 5x\), we will use the properties of exponents and basic arithmetic.
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Divide the coefficients: \[ -25 / 5 = -5 \]
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Use the quotient rule for exponents: According to the properties of exponents, when you divide like bases, you subtract the exponents: \[ x^8 / x^1 = x^{8-1} = x^7 \]
Putting it all together, we have: \[ -25x^8 / 5x = -5 \cdot x^7 = -5x^7 \]
Therefore, the simplified expression is \(-5x^7\).
The correct option is: option b: -5x^7.