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

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