解:$(1)(-3\ \mathrm {m^3}n)^2 = (-3)^2\ \mathrm {·}(\mathrm {m^3})^2\ \mathrm {·}n^2 = 9\ \mathrm {m}^6n^2$
$(2)(-\frac 13a^3b^2)^3 = (-\frac 13)^3\ \mathrm {·}(a^3)^3\ \mathrm {·}(b^2)^3 = -\frac 1{27}a^9b^6$
$(3)(x^3)^5\ \mathrm {·}x^4 = x^{15}\ \mathrm {·}x^4 = x^{15+4} = x^{19}$
$(4)(-\frac 13 ×10^4)^5 = (-\frac 13)^5 ×(10^4)^5 = -\frac 1{243} ×10^{20} = -\frac {10^{20}}{243}$