To multiply the expressions \(5a^2b^5c^3\) and \(-4a^7c^5\), we can follow these steps:
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Multiply the coefficients: \[ 5 \cdot (-4) = -20 \]
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Multiply the variables by adding their exponents:
- For \(a\): \[ a^2 \cdot a^7 = a^{2+7} = a^9 \]
- For \(b\): \[ b^5 \text{ (there is no } b \text{ in the second expression, so it remains as } b^5) \]
- For \(c\): \[ c^3 \cdot c^5 = c^{3+5} = c^8 \]
Now, combine all the results: \[ -20a^9b^5c^8 \]
Thus, the final answer is: \[ \text{negative } 20a^9b^5c^8 \]
The response that corresponds to this result is: \[ \text{negative } 20 a^{9} b^{5} c^{8} \]