To simplify the expression \(-12x^5y^2(10x^3y^4)\), you can use the distributive property by multiplying the coefficients and adding the exponents for like bases.
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Multiply the coefficients: \(-12 \times 10 = -120\)
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Add the exponents for \(x\): \(x^5 \cdot x^3 = x^{5+3} = x^8\)
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Add the exponents for \(y\): \(y^2 \cdot y^4 = y^{2+4} = y^6\)
Now, combine these results:
\[ -12x^5y^2(10x^3y^4) = -120x^8y^6 \]
So, the simplified expression is:
\[ \boxed{-120x^8y^6} \]