2. Упростите выражения: a) \(\frac{(a^3)^{-2} \cdot (a^{-7})^{-1}}{a^{-3}} б) \left\(-\frac{2a}{3b^3}\right\)^{-2} : \(\left\)\(-\frac{a^{-2}}{4b^5}\right\)^{-1} a) \(\frac{(a^{-2})^{-4} \cdot (a^3)^{-2}}{a^{-2}}\) б) \(\left\)\(\frac{3a^{-1}}{5b^2}\right\)^{-2} : \(\left\)\(-\frac{a}{25b^5}\right\)^{-1}

2. Упрощение выражений:

1. а) \(\frac{(a^3)^{-2} \cdot (a^{-7})^{-1}}{a^{-3}} = \frac{a^{-6} \cdot a^7}{a^{-3}} = \frac{a^1}{a^{-3}} = a^{1 - (-3)} = a^4\)
2. б) \(\left(-\frac{2a}{3b^3}\right)^{-2} : \left(-\frac{a^{-2}}{4b^5}\right)^{-1} = \left(-\frac{3b^3}{2a}\right)^2 : \left(-\frac{4b^5}{a^{-2}}\right) = \frac{9b^6}{4a^2} : (-4b^5a^2) = \frac{9b^6}{4a^2} \cdot \left(-\frac{1}{4a^2b^5}\right) = -\frac{9b}{16a^4}\)
3. а) \(\frac{(a^{-2})^{-4} \cdot (a^3)^{-2}}{a^{-2}} = \frac{a^8 \cdot a^{-6}}{a^{-2}} = \frac{a^2}{a^{-2}} = a^{2 - (-2)} = a^4\)
4. б) \(\left(\frac{3a^{-1}}{5b^2}\right)^{-2} : \left(-\frac{a}{25b^5}\right)^{-1} = \left(\frac{5b^2}{3a^{-1}}\right)^2 : \left(-\frac{25b^5}{a}\right) = \left(\frac{5b^2a}{3}\right)^2 \cdot \left(-\frac{a}{25b^5}\right) = \frac{25b^4a^2}{9} \cdot \left(-\frac{a}{25b^5}\right) = -\frac{a^3}{9b}\)

Ответ: а) \(a^4\); б) \(-\frac{9b}{16a^4}\); а) \(a^4\); б) \(-\frac{a^3}{9b}\).