Multiply. \[ -4 w^{2}(-7 w) \] Simplify your answer as much as possible.

To multiply \(-4 w^{2}(-7 w)\), you can start by multiplying the coefficients and then the variables separately. First, multiply the coefficients: \(-4\) and \(-7\) yield \(28\) because the product of two negative numbers is positive. Next, multiply the variable parts: \(w^{2}\) and \(w\) give \(w^{3}\) because when you multiply powers of the same base, you add their exponents (2 + 1 = 3). Putting it all together, the simplified result is: \[ 28w^{3} \]