Упростите выражение: a) $$2x^9 \cdot (-4a^2x^3)^2$$; б) $$(-a^3b^6)^5 \cdot 5ab^4$$; в) $$(-0.2m^3np^4)^2 \cdot 25mn^3p$$; г) $$-1\frac{2}{3}a^3b^6 \cdot (-\frac{3}{5}a^2b)^3$$; д) $$3\frac{1}{2}x^4y \cdot (\frac{4}{7}x^2y^3)^2$$; e) $$(-\frac{1}{3}a^5b^9)^3 \cdot (-3ab)^4$$.

a) $$2x^9 \cdot (-4a^2x^3)^2 = 2x^9 \cdot (16a^4x^6) = 32a^4x^{15}$$.

б) $$(-a^3b^6)^5 \cdot 5ab^4 = (-1)^5a^{3\cdot5}b^{6\cdot5} \cdot 5ab^4 = -a^{15}b^{30} \cdot 5ab^4 = -5a^{16}b^{34}$$.

в) $$(-0.2m^3np^4)^2 \cdot 25mn^3p = (0.04m^6n^2p^8) \cdot 25mn^3p = 0.04 \cdot 25 m^6 \cdot m n^2 \cdot n^3 p^8 \cdot p = m^7n^5p^9$$.

г) $$-1\frac{2}{3}a^3b^6 \cdot (-\frac{3}{5}a^2b)^3 = -\frac{5}{3}a^3b^6 \cdot (-\frac{27}{125}a^6b^3) = \frac{5}{3} \cdot \frac{27}{125} a^3 \cdot a^6 b^6 \cdot b^3 = \frac{9}{25}a^9b^9$$.

д) $$3\frac{1}{2}x^4y \cdot (\frac{4}{7}x^2y^3)^2 = \frac{7}{2}x^4y \cdot (\frac{16}{49}x^4y^6) = \frac{7}{2} \cdot \frac{16}{49} x^4 \cdot x^4 y \cdot y^6 = \frac{8}{7}x^8y^7$$.

e) $$(-\frac{1}{3}a^5b^9)^3 \cdot (-3ab)^4 = (-\frac{1}{27}a^{15}b^{27}) \cdot (81a^4b^4) = -\frac{1}{27} \cdot 81 a^{15} \cdot a^4 b^{27} \cdot b^4 = -3a^{19}b^{31}$$.