1. Упростите выражение:

Решение:

1. \( x^3 \cdot (-x^4) = -x^{3+4} = -x^7 \)
2. \( x^3 \cdot \left(-\frac{1}{x}\right)^4 = x^3 \cdot \frac{1}{x^4} = \frac{1}{x} \)
3. \( (a^2)^5 \cdot a^5 = a^{10} \cdot a^5 = a^{15} \)
4. \( (a^2 \cdot a^5)^2 = (a^7)^2 = a^{14} \)
5. \( (c^4)^2 \cdot (c^2)^3 = c^8 \cdot c^6 = c^{14} \)
6. \( (c \cdot c^2)^3 \cdot (c^2 \cdot c^3)^2 = (c^3)^3 \cdot (c^5)^2 = c^9 \cdot c^{10} = c^{19} \)
7. \( y^{12} : (y^6)^2 = y^{12} : y^{12} = 1 \)
8. \( (y^4)^5 : (y^4)^2 = y^{20} : y^8 = y^{12} \)
9. \( (y \cdot y^2)^3 : (y \cdot y^3)^2 = (y^3)^3 : (y^4)^2 = y^9 : y^8 = y \)