Start with
(-5^5 y^4 z^-5)^6 /(2^-2 y^-2 z^3)(−55y4z−5)62−2y−2z3
To avoid confusion, rewrite as
((-1)*5^5 y^4 z^-5)^6 /(2^-2 y^-2 z^3)((−1)⋅55y4z−5)62−2y−2z3
Now apply exponent rule (a^n)^m=a^(nm)(an)m=anm
((-1)^6*5^30 y^24 z^-30) /(2^-2 y^-2 z^3)(−1)6⋅530y24z−302−2y−2z3
Note that (-1)^6=1(−1)6=1 because 6 is even so our expression is now
(5^30 y^24 z^-30) /(2^-2 y^-2 z^3)530y24z−302−2y−2z3
Using exponent laws we know that 1/2^-2= 2^2/112−2=221
(2^2*5^30 y^24 z^-30) /(y^-2 z^3)22⋅530y24z−30y−2z3
Exponent laws also tell us that y^24/y^-2=y^(24--2)=y^(24+2)=y^26y24y−2=y24−−2=y24+2=y26 so we can write
(2^2*5^30 y^26 z^-30) /z^322⋅530y26z−30z3
Finally z^-30/z^3=1/z^(3--30)=1/z^(3+30)=1/z^33z−30z3=1z3−−30=1z3+30=1z33 so the answer is
(2^2*5^30 y^26) /z^3322⋅530y26z33
