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

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

Ответ: $$\frac{a}{b^6}$$