a) $$(5x^2y^3)^2 = 5^2 * (x^2)^2 * (y^3)^2 = 25x^4y^6$$
б) $$(-4ax^3)^3 = (-4)^3 * a^3 * (x^3)^3 = -64a^3x^9$$
в) $$(-2m^3n^2)^4 = (-2)^4 * (m^3)^4 * (n^2)^4 = 16m^{12}n^8$$
г) $$(-a^2bc^3)^5 = (-1)^5 * (a^2)^5 * b^5 * (c^3)^5 = -a^{10}b^5c^{15}$$