( x 7^ ( − y 8^ z 5^ ) 2 ^) 3 simplify

the ^ is written in front of the exponent, so I will interpret your typing as:

( x^7 (-y^8 z^5)^2 )^3
= ( x^7(-y^16 z^10)^3
= ( - x^7 y^16 z^10)^3
= - x^21 y^48 z^ 30

the problem is the -y^8
If you meant (-y)^8, then the result would be +