12. $$\frac{(a^{-2}b^3)^2}{a^{-1}b} =$$

$$\frac{(a^{-2}b^3)^2}{a^{-1}b} = \frac{a^{-2 \cdot 2}b^{3 \cdot 2}}{a^{-1}b} = \frac{a^{-4}b^6}{a^{-1}b} = a^{-4 - (-1)} b^{6-1} = a^{-4 + 1}b^5 = a^{-3}b^5 = \frac{b^5}{a^3}$$

Ответ: $$\frac{b^5}{a^3}$$