We are asked to simplify the expression $(-2x^2y^3z^4)(-4x^3yz^{-8})(5xy^2z^2)$.

1. Problem Description

We are asked to simplify the expression $(-2x^2y^3z^4)(-4x^3yz^{-8})(5xy^2z^2)$.

2. Solution Steps

First, we multiply the coefficients:

$(-2)(-4)(5) = 40$.

Next, we multiply the $x$ terms. Recall that $x^a x^b = x^{a+b}$. We have $x^2 x^3 x = x^{2+3+1} = x^6$.

Next, we multiply the $y$ terms. We have $y^3 y y^2 = y^{3+1+2} = y^6$.

Finally, we multiply the $z$ terms. We have $z^4 z^{-8} z^2 = z^{4-8+2} = z^{-2}$.

Putting it all together, we have

$40x^6y^6z^{-2}$. We can also write $z^{-2}$ as $\frac{1}{z^2}$.

Therefore, the final expression is $\frac{40x^6y^6}{z^2}$.

3. Final Answer

$\frac{40x^6y^6}{z^2}$