354. a) $$(2ax^2)^2 \cdot (ax)^3$$; в) $$(-2x^2y^3)^2 \cdot (-5xy^2)^3$$; б) $$(3nz^3)^2 \cdot (\frac{1}{3}nzx)^3$$; г) $$(-\frac{2}{3}ax^2)^3 \cdot (\frac{3}{5}a^3x)^2$$; д) $$3x^2 \cdot (-5x^3y^4)^2$$; е) $$(-a^6b^3)^7 \cdot 6a^3b^4$$; ё) $$0,5mn^4 \cdot (-2m)^5$$; ж) $$(-0,1x^2y)^4 \cdot 1000xy^2$$.

Решим данные примеры: a) $$(2ax^2)^2 \cdot (ax)^3 = 2^2 \cdot a^2 \cdot (x^2)^2 \cdot a^3 \cdot x^3 = 4a^2x^4 \cdot a^3x^3 = 4a^{2+3}x^{4+3} = \textbf{4a^5x^7}$$ б) $$(3nz^3)^2 \cdot (\frac{1}{3}nzx)^3 = 3^2 \cdot n^2 \cdot (z^3)^2 \cdot (\frac{1}{3})^3 \cdot n^3 \cdot z^3 \cdot x^3 = 9n^2z^6 \cdot \frac{1}{27}n^3z^3x^3 = \frac{9}{27}n^{2+3}z^{6+3}x^3 = \frac{1}{3}n^5z^9x^3 = \textbf{$$\frac{1}{3}n^5x^3z^9$$}$$ в) $$(-2x^2y^3)^2 \cdot (-5xy^2)^3 = (-2)^2 \cdot (x^2)^2 \cdot (y^3)^2 \cdot (-5)^3 \cdot x^3 \cdot (y^2)^3 = 4x^4y^6 \cdot (-125)x^3y^6 = -500x^{4+3}y^{6+6} = \textbf{-500x^7y^{12}}$$ г) $$(-\frac{2}{3}ax^2)^3 \cdot (\frac{3}{5}a^3x)^2 = (-\frac{2}{3})^3 \cdot a^3 \cdot (x^2)^3 \cdot (\frac{3}{5})^2 \cdot (a^3)^2 \cdot x^2 = -\frac{8}{27}a^3x^6 \cdot \frac{9}{25}a^6x^2 = -\frac{8 \cdot 9}{27 \cdot 25}a^{3+6}x^{6+2} = -\frac{8}{3 \cdot 25}a^9x^8 = \textbf{-\frac{8}{75}a^9x^8}$$ д) $$3x^2 \cdot (-5x^3y^4)^2 = 3x^2 \cdot (-5)^2 \cdot (x^3)^2 \cdot (y^4)^2 = 3x^2 \cdot 25x^6y^8 = 75x^{2+6}y^8 = \textbf{75x^8y^8}$$ e) $$(-a^6b^3)^7 \cdot 6a^3b^4 = (-1)^7 \cdot (a^6)^7 \cdot (b^3)^7 \cdot 6a^3b^4 = -a^{42}b^{21} \cdot 6a^3b^4 = -6a^{42+3}b^{21+4} = \textbf{-6a^{45}b^{25}}$$ ё) $$0,5mn^4 \cdot (-2m)^5 = 0,5mn^4 \cdot (-2)^5m^5 = 0,5mn^4 \cdot (-32)m^5 = -16m^{1+5}n^4 = \textbf{-16m^6n^4}$$ ж) $$(-0,1x^2y)^4 \cdot 1000xy^2 = (-0,1)^4 \cdot (x^2)^4 \cdot y^4 \cdot 1000xy^2 = 0,0001x^8y^4 \cdot 1000xy^2 = 0,1x^{8+1}y^{4+2} = \textbf{0,1x^9y^6}$$