To simplify the expression \( 4a^6b^5c^4 \times -7b^7c^6 \), you can multiply the coefficients and combine the variables accordingly.
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Multiply the coefficients: \( 4 \times -7 = -28 \)
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Combine the variables:
- For \( b \): \( b^5 \times b^7 = b^{5+7} = b^{12} \)
- For \( c \): \( c^4 \times c^6 = c^{4+6} = c^{10} \)
Putting it all together, we get:
\[ 4a^6b^5c^4 \times -7b^7c^6 = -28a^6b^{12}c^{10} \]
So, the simplified expression is:
\[ -28a^6b^{12}c^{10} \]