a) $$(3x^2)^3 = 3^3 \cdot (x^2)^3 = 27x^{2\times3} = 27x^6$$;
b) $$(4m)^2 = 4^2 \cdot m^2 = 16m^2$$;
c) $$(-2a^4b^2)^3 = (-2)^3 \cdot (a^4)^3 \cdot (b^2)^3 = -8a^{4\times3}b^{2\times3} = -8a^{12}b^6$$;
d) $$(-3x^2y)^2 = (-3)^2 \cdot (x^2)^2 \cdot y^2 = 9x^{2\times2}y^2 = 9x^4y^2$$;
e) $$(-a^2bc^3)^5 = (-1)^5 \cdot (a^2)^5 \cdot b^5 \cdot (c^3)^5 = -a^{2\times5}b^5c^{3\times5} = -a^{10}b^5c^{15}$$;
f) $$(-a^3b^2c)^2 = (-1)^2 \cdot (a^3)^2 \cdot (b^2)^2 \cdot c^2 = a^{3\times2}b^{2\times2}c^2 = a^6b^4c^2$$.