To multiply the expressions \( 5a^2b^5c^3 \) and \(-4a^7c^5\), we will follow the properties of operations, particularly the distributive property and the properties of exponents.
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Multiply the coefficients:
- The coefficients are \(5\) and \(-4\).
- Multiplying these gives: \[ 5 \times -4 = -20. \]
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Multiply the variables:
- For variable \(a\): \[ a^2 \times a^7 = a^{2+7} = a^9 \quad \text{(adding the exponents)}. \]
- For variable \(b\):
- Since \(b\) only appears in the first term, it remains as is: \[ b^5. \]
- For variable \(c\): \[ c^3 \times c^5 = c^{3+5} = c^8 \quad \text{(adding the exponents)}. \]
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Combine the results: Combining all parts, we have: \[ -20a^9b^5c^8. \]
Thus, the result of multiplying \( 5a^2b^5c^3 \) and \(-4a^7c^5\) is: \[ \boxed{-20a^9b^5c^8}. \]