z-[2z-[3z-(4z-5z)-6z-7z)-8z

To simplify the expression z-[2z-[3z-(4z-5z)-6z-7z)-8z], we can start by simplifying the innermost parentheses.

Inside the first set of parentheses, we have (4z-5z) which simplifies to -z.

Now, let's substitute -z back into the expression:
z-[2z-[3z-(-z)-6z-7z)-8z].

Inside the second set of parentheses, we have -z.

Now, let's substitute -z back into the expression:
z-[2z-[-z-6z-7z)-8z].

Inside the third set of parentheses, we have -z-6z-7z, which simplifies to -14z.
Now, let's substitute -14z back into the expression:
z-[2z-[-14z)-8z].

Inside the second set of parentheses, we have -14z.

Now, let's substitute -14z back into the expression:
z-[2z-(-14z-8z)].

Inside the first set of parentheses, we have -14z + 8z, which simplifies to -6z.

Now, let's substitute -6z back into the expression:
z-[2z-(-6z)].

Inside the parentheses, we have -6z.

Now, let's simplify the expression:
z-2z+6z.

Combining like terms, we get z+4z, which simplifies to 5z.

So, the simplified expression is 5z.