Chapter 1 - Introduction to Algebraic Expressions - 1.8 Exponential Notation and Order of Operations - 1.8 Exercise Set - Page 67: 118

$-4z$

Using order of operations, the given expression, $ z-\{2z-[3z-(4z-5z)-6z]-7z\}-8z $, simplifies to \begin{array}{l}\require{cancel} z-\{2z-[3z-(-z)-6z]-7z\}-8z \\\\= z-\{2z-[3z+z-6z]-7z\}-8z \\\\= z-\{2z-[-2z]-7z\}-8z \\\\= z-\{2z+2z-7z\}-8z \\\\= z-\{-3z\}-8z \\\\= z+3z-8z \\\\= 4z-8z \\\\= -4z .\end{array}