2. a) (-10p^2n^5) \(\cdot\) \(\frac{1}{5}n^2p^9\); 6) 81a^{13}c^2d : (-9ac^2).

Решение:

1. \( (-10p^2n^5) \cdot (\frac{1}{5}n^2p^9) = (-10 \cdot \frac{1}{5})(p^2 \cdot p^9)(n^5 \cdot n^2) = -2p^{2+9}n^{5+2} = -2p^{11}n^7 \)
2. \( 81a^{13}c^2d : (-9ac^2) = \frac{81}{-9} \cdot \frac{a^{13}}{a} \cdot \frac{c^2}{c^2} \cdot \frac{d}{1} = -9a^{13-1} \cdot c^{2-2} \cdot d = -9a^{12}c^0d = -9a^{12}d \)

Ответ: а) -2p¹¹n⁷; б) -9a¹²d.