To multiply the expressions \(5xy^4z^5\) and \(8x^7z^2\), you multiply the coefficients and then combine like variables.
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Multiply the coefficients: \(5 \times 8 = 40\)
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Combine the variables:
- For \(x\): \(x^1 \cdot x^7 = x^{1+7} = x^8\)
- For \(y\): \(y^4\) (there is no \(y\) in the second expression, so it remains as \(y^4\))
- For \(z\): \(z^5 \cdot z^2 = z^{5+2} = z^7\)
Now combine all these components:
\[ 5xy^4z^5 \times 8x^7z^2 = 40x^8y^4z^7 \]
So the final result is:
\[ \boxed{40x^8y^4z^7} \]