Задание 42. Возведите одночлен в степень 1) (a²b³)5 = (a2)5 - (63)5 = a10615 2) (x4y²)³ = 3) (2m5n3)2 = 4) (4ab4)3 = 5) (-5c³k³)2 = 6) (-3mn²)4= 7) (-2xy) = 8) (-4m²n)³ = 9) (-2a2b3)5 = 10) (-a)= 11) (-5m4n²)² = 12) (-6q5p3)2 = 13) --xy 3 4 3 = 14) (-0,2c2p4)4 = 2 15) (-a³0,46) = 1 4 3

Ответ:

1. (x⁴y²)³ = x^4\cdot3y^2\cdot3 = x¹²y⁶

2. (2m⁵n³)² = 2²m^5\cdot2n^3\cdot2 = 4m¹⁰n⁶

3. (4ab⁴)³ = 4³a³b^4\cdot3 = 64a³b¹² = 64a³b¹²

4. (-5c³k³)² = (-5)²c^3\cdot2k^3\cdot2 = 25c⁶k⁶ = 25c⁶k⁶

5. (-3mn²)⁴ = (-3)⁴m⁴n^2\cdot4 = 81m⁴n⁸ = 81m⁴n⁸

6. (-2xy)⁶ = (-2)⁶x⁶y⁶ = 64x⁶y⁶ = 64x⁶y⁶

7. (-4m²n)³ = (-4)³m^2\cdot3n³ = -64m⁶n³ = -64m⁶n³

8. (-2a²b³)⁵ = (-2)⁵a^2\cdot5b^3\cdot5 = -32a¹⁰b¹⁵ = -32a¹⁰b¹⁵

9. \(\left(-\frac{1}{3}a^{5}y^{3}\right)^{4} = \left(-\frac{1}{3}\right)^{4}a^{5\cdot4}y^{3\cdot4} = \frac{1}{81}a^{20}y^{12}\) = \(\frac{1}{81}a^{20}y^{12}\)

10. (-5m⁴n²)² = (-5)²m^4\cdot2n^2\cdot2 = 25m⁸n⁴ = 25m⁸n⁴

11. (-6q⁵p³)² = (-6)²q^5\cdot2p^3\cdot2 = 36q¹⁰p⁶ = 36q¹⁰p⁶

12. \(\left(\frac{2}{3}xy^{4}\right)^{3} = \left(\frac{2}{3}\right)^{3}x^{3}y^{4\cdot3} = \frac{8}{27}x^{3}y^{12}\) = \(\frac{8}{27}x^{3}y^{12}\)

13. (-0.2c²p⁴)⁴ = (-0.2)⁴c^2\cdot4p^4\cdot4 = 0.0016c⁸p¹⁶ = 0.0016c⁸p¹⁶

14. \(\left(\frac{1}{4}a^{3} \cdot 0,4b^{7}\right)^{3} = \left(\frac{1}{4} \cdot 0,4\right)^{3}a^{3\cdot3}b^{7\cdot3} = (0.1)^{3}a^{9}b^{21} = 0.001a^{9}b^{21}\) = \(0.001a^{9}b^{21}\)

Ответ: