Упростите выражения 1) 20a^8 * (9a) ^2 2) (-b^5) ^4*12b^6 3) (3m^6n^3) ^4 * (-1|18 m^9n) 4) (0.2x^7y^8) ^3*6x^2y^2 5) (-1|2 ab^4) ^3 * (4a^6) ^2 6) (-2|3x^2y) ^5 * (-3|4xy^2) ^2

Упростим выражения учитывая свойства степеней a^m * a^n = a^ (m + n), (a^m) ^n = a^ (m * n):

1) 20 а^8 * (9 а) ^2 = 20a^8 * 81a^2 = 81 * 20 * a^ (8 + 2) = 1620a^10;

2) (-b^5) ^4 * 12b^6 = b^ (5 * 4) * 12b^6 = b^9 * 12b^6: = 12b^ (9 + 6) = 12b^15;

3) (3m^6n^3) ^4 * (-1/18m^9n) = 3^4m^24n^12 * (-1/18m^9n) = - 81/18m^33n^13 = - 4,5m^33n^13;

4) (0,2x^7y^8) ^3 * 6x^2y^2 = 0,008x^21y^24 * 6x^2y^2 = 0,048x^23y^26;

5) (-1/2ab^4) ^3 * (4a^6) ^2 = - 1/8a^3b^12 * 16a^12 = - 2a^15b^12;

6) (-2/3x^2y) ^5 * (-3/4xy^2) ^2 = - 32/243x^19y^5 * 9/16x^2y^4 = - 2/27x^21y^9.