Verified answer

(a^m)^m = a^(mn)

a^m*a^n = a^(m+n)

(a^-m) = 1/(a^m)

(-1/3)^(-10) * 27^(-3) = (-3^(-1))^(-10) * (3^3)^(-3) = (-1)^(-10) * 3^(-1*-10) * 3^(3*-3) = 3^10*3^-9 = 3

(0.2)^(-4) * 25^(-2) = {0.2=2/10=1/5=5^(-1)} = (5^(-1))^(-4) * (5^2)^(-2) = 5^(4 - 4 ) = 5^0 = 1

(0.125)^(-2) = {125/1000=1/8=8^(-1)} = (8^(-1))^(-2) = 8^(-1)*(-2) = 8^2 = 64

3 + 1 + 64 = 67