1.
a^(-2)*b^2*[a^2*b^(-2)]^(-3)
=a^(-2)*b^2*a^(-6)*b^6
=a^(-2-6)*b^(2+6)
=a^(-8)*b^8;
2.
[1-x/(x-1)]÷[1/(x^2-2)]
=[(x-1-x)/(x-1)]*(x^2-2)
=-(x^2-2)/(x-1)
=(2-x^2)/(x-1).