2. Упростите выражение: a) \(\frac{(a^{-2})^{-4} ⋅ (a^3)^{-2}}{(a^{-3})^{-1} : (a^{-1})^3}\); б) \(\left(\frac{3a^{-1}}{5b^2}\right)^{-2} ⋅ \left(\frac{a}{25b^5}\right)^{-1}\)

2. Упрощение выражений:

1. а) \( \frac{(a^{-2})^{-4} ⋅ (a^3)^{-2}}{(a^{-3})^{-1} : (a^{-1})^3} = \frac{a^{(-2) \cdot (-4)} ⋅ a^{3 \cdot (-2)}}{a^{(-3) \cdot (-1)} : a^{(-1) \cdot 3}} = \frac{a^8 ⋅ a^{-6}}{a^3 : a^{-3}} = \frac{a^{8+(-6)}}{a^{3-(-3)}} = \frac{a^2}{a^6} = a^{2-6} = a^{-4} = \frac{1}{a^4} \)
2. б) \( \left(\frac{3a^{-1}}{5b^2}\right)^{-2} ⋅ \left(\frac{a}{25b^5}\right)^{-1} = \left(\frac{5b^2}{3a^{-1}}\right)^{2} ⋅ \left(\frac{25b^5}{a}\right) = \left(\frac{5b^2 a}{3}\right)^{2} ⋅ \frac{25b^5}{a} = \frac{25b^4 a^2}{9} ⋅ \frac{25b^5}{a} = \frac{25 ⋅ 25 ⋅ a^2 ⋅ b^4 ⋅ b^5}{9 ⋅ a} = \frac{625 a^{2-1} b^{4+5}}{9} = \frac{625 a b^9}{9} \)

Ответ: а) \(a^{-4}\); б) \(\frac{625ab^9}{9}\).