To simplify the expression \( \frac{5a^4 b^2 c}{a^3 b} \), we can start by simplifying the fraction itself:
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Split the fraction: \[ \frac{5a^4 b^2 c}{a^3 b} = 5c \cdot \frac{a^4 b^2}{a^3 b} \]
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Simplify \( \frac{a^4 b^2}{a^3 b} \) by canceling powers of \( a \) and \( b \):
- For \( a \): \( a^4 / a^3 = a^{4-3} = a^1 = a \)
- For \( b \): \( b^2 / b = b^{2-1} = b^1 = b \)
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Now we have: \[ \frac{a^4 b^2}{a^3 b} = ab \]
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Now substitute this back into the expression: \[ 5c \cdot ab = 5abc \]
If we want to solve for \( c \) in the original expression, we can think of it as: \[ c = \frac{5abc}{ab} \] which simplifies to: \[ c = 5 \]
However, since 5 is not one of the answer choices (the options are -1, 6, 1, 2, 0), we might have misunderstood the original question.
If we were supposed to simplify the coefficients or represent them in terms of their algebraic structure, then this information implies \( c \) could take any numerical value that balances the equation given other conditions.
After reassessing the options concluded above, if there are no constraints after \( c \), then among the options given, we need to determine the value \( c \) holds. The value can depend on things we have not analyzed here based on provided format. Therefore, based on representation simplicity, and all transformations have been tracked as relations in \( c \), hence options could vary.
So the expression can be normalized more clearly representing \( c = 1 \) if dependency on others held, otherwise \( c \) might vary as defined.
Thus the closest meaningful simplified constant for \( c \) amongst the options could be \( C. 1 \).
Final answer: C. 1