\(25^{1 - x} \times 5^{x + 2} \div (\frac{1}{125})^{x} = 625^{-1}\) \((5^2)^{(1 - x)} \times 5^{(x + 2)} \div (5^{-3})^x = (5^4)^{-1}\) \(5^{2 - 2x} \times 5^{x + 2} \div 5^{-3x} = 5^{-4}\) \(5^{(2 - 2x) + (x + 2) - (-3x)} = 5^{-4}\) Equating bases, we have \(2 - 2x + x + 2 + 3x = -4\) \(4 + 2x = -4 \implies 2x = -4 - 4\) \(2x = -8\) \(x = -4\)