To find the product of \((-7u^2)(4u^2)\), you can multiply the coefficients and the variables separately.
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Multiply the coefficients: \(-7 \times 4 = -28\)
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Multiply the variable parts: \(u^2 \times u^2 = u^{2+2} = u^4\)
Now, combine the two results:
\[ (-7u^2)(4u^2) = -28u^4 \]
Thus, the simplified answer is:
\[ \boxed{-28u^4} \]