b^{-10} \cdot (5b^4)^3 / (5b^3)^{12} = 125

The expression is \(b^{-10} \cdot (5b^4)^3 / (5b^3)^{12}\).

Simplify the terms: \((5b^4)^3 = 5^3 b^{12} = 125 b^{12}\) and \((5b^3)^{12} = 5^{12} b^{36}\).

Substitute and simplify: \(b^{-10} \cdot 125 b^{12} / (5^{12} b^{36}) = (125 b^2) / (5^{12} b^{36}) = 125 / (5^{12} b^{34})\).

The given equation \(125 / (5^{12} b^{34}) = 125\) implies \(5^{12} b^{34} = 1\), which is not generally true for all \(b\).