Answer
$$-\frac{2z^2}{3x^3y^2}
.
$$
Work Step by Step
We divide by the monomial as follows
$$
(-144x^2z^3) \div (216x^5y^2z)=\frac{-144x^2z^3}{216x^5y^2z}\\
=\frac{-72\cdot 2x^2z^3}{72\cdot 3x^5y^2z}=-\frac{2z^2}{3x^3y^2}
.
$$
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