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.