8. Возведите в степень:

Решение:

Используем свойство степени \( (ab)^n = a^n b^n \) и \( (a^m)^n = a^{mn} \).

1. \( (xy)^4 = x^4 y^4 \)
2. \( (2x)^3 = 2^3 x^3 = 8x^3 \)
3. \( (-5x)^3 = (-5)^3 x^3 = -125x^3 \)
4. \( (-0.2xy)^4 = (-0.2)^4 x^4 y^4 = 0.0016x^4 y^4 \)
5. \( (abc)^5 = a^5 b^5 c^5 \)
6. \( (3a)^2 = 3^2 a^2 = 9a^2 \)
7. \( (-10ab)^2 = (-10)^2 a^2 b^2 = 100a^2 b^2 \)
8. \( (-0.5bd)^3 = (-0.5)^3 b^3 d^3 = -0.125b^3 d^3 \)
9. \( (nm)^5 = n^5 m^5 \)
10. \( (-3y)^4 = (-3)^4 y^4 = 81y^4 \)
11. \( (10xy)^2 = 10^2 x^2 y^2 = 100x^2 y^2 \)
12. \( (-am)^3 = (-a)^3 m^3 = -a^3 m^3 \)
13. \( (c^4)^2 = c^{4 \times 2} = c^8 \)
14. \( (c^2)^4 = c^{2 \times 4} = c^8 \)
15. \( (xyz)^2 = x^2 y^2 z^2 \)
16. \( (-2ax)^3 = (-2)^3 a^3 x^3 = -8a^3 x^3 \)
17. \( (-2abx)^4 = (-2)^4 a^4 b^4 x^4 = 16a^4 b^4 x^4 \)
18. \( (-xn)^4 = (-x)^4 n^4 = x^4 n^4 \)