trying to re-learn algebra, cannot figure out how the answer is 35. Would
appreciate your help in explaining/showing the breakdown of the problem.

8-9[(-39)/(-13)+7(-2)-(-2)^3

here's what i did:
8-9[(-39)/(-13)+7(-2)-(-8)]=8-9[3+(-14)-(-8)]
                           =8-9[-11-(-8)]
                           =8-9[-19]     <---  THERE"S YOUR ERROR!!!
                           =8-171        <---  WRONG
                           =-163         <---  WRONG

Here's the correct way:

8-9[(-39)/(-13)+7(-2)-(-8)]=8-9[3+(-14)-(-8)]
                           =8-9[-11-(-8)]
                           =8-9[-11+8]
                           =8-9[-3]
                           =8+27
                           =35

You need to learn that -(-8) becomes +8 and -9[-3] becomes +27.

Edwin