1. Упростите выражение: a) (a^5)^3 : a^{10} * a; б) xy^2 - 13xy^2 + 5xy^2; в) (3x^2y)^4 : (3xy^2)^2; г) (z^8)^4 / (2(z^6)^7)

a) (a^5)^3 : a^{10} * a = a^{15} : a^{10} * a = a^{15-10} * a = a^5 * a = a^{5+1} = a^6 б) xy^2 - 13xy^2 + 5xy^2 = (1 - 13 + 5)xy^2 = -7xy^2 в) (3x^2y)^4 : (3xy^2)^2 = (3^4 * (x^2)^4 * y^4) : (3^2 * x^2 * (y^2)^2) = (81x^8y^4) : (9x^2y^4) = (81/9) * (x^8/x^2) * (y^4/y^4) = 9x^6 г) (z^8)^4 / (2(z^6)^7) = z^{32} / (2 * z^{42}) = (1/2) * z^{32-42} = (1/2) * z^{-10} = 1 / (2z^{10})