1. Упростите выражение: 1) a) (-a)^5 \cdot a^3; б) -a^5 \cdot a^3; в) a^5 \cdot (-a)^3; г) -(a^5) \cdot (-a)^3; 2) a) (x^8)^7 \cdot x^3; б) (x^8 \cdot x^7)^3; в) x^8 \cdot (x^8)^8; г) (x \cdot x^7)^7; 3) a) (y^3)^4 \cdot (y^4)^3; б) (y^4 \cdot y)^4 \cdot (y^4 \cdot y)^3; в) (y^3)^2 \cdot (y^5 \cdot y^2)^2; 4) a) c^{12} : (c^4)^3; б) (c^2)^9 : (c^2)^8; в) (c^3 \cdot c)^4 : (c^4 \cdot c)^3.

1) a) $$(-a)^5 \cdot a^3 = -a^5 \cdot a^3 = -a^{5+3} = -a^8$$ б) $$-a^5 \cdot a^3 = -a^{5+3} = -a^8$$ в) $$a^5 \cdot (-a)^3 = -a^5 \cdot a^3 = -a^{5+3} = -a^8$$ г) $$-(a^5) \cdot (-a)^3 = -a^5 \cdot (-1) \cdot a^3 = a^5 \cdot a^3 = a^{5+3} = a^8$$ 2) a) $$(x^8)^7 \cdot x^3 = x^{8\cdot7} \cdot x^3 = x^{56} \cdot x^3 = x^{56+3} = x^{59}$$ б) $$(x^8 \cdot x^7)^3 = (x^{8+7})^3 = (x^{15})^3 = x^{15\cdot3} = x^{45}$$ в) $$x^8 \cdot (x^8)^8 = x^8 \cdot x^{8\cdot8} = x^8 \cdot x^{64} = x^{8+64} = x^{72}$$ г) $$(x \cdot x^7)^7 = (x^{1+7})^7 = (x^8)^7 = x^{8\cdot7} = x^{56}$$ 3) a) $$(y^3)^4 \cdot (y^4)^3 = y^{3\cdot4} \cdot y^{4\cdot3} = y^{12} \cdot y^{12} = y^{12+12} = y^{24}$$ б) $$(y^4 \cdot y)^4 \cdot (y^4 \cdot y)^3 = (y^{4+1})^4 \cdot (y^{4+1})^3 = (y^5)^4 \cdot (y^5)^3 = y^{5\cdot4} \cdot y^{5\cdot3} = y^{20} \cdot y^{15} = y^{20+15} = y^{35}$$ в) $$(y^3)^2 \cdot (y^5 \cdot y^2)^2 = y^{3\cdot2} \cdot (y^{5+2})^2 = y^6 \cdot (y^7)^2 = y^6 \cdot y^{7\cdot2} = y^6 \cdot y^{14} = y^{6+14} = y^{20}$$ 4) a) $$c^{12} : (c^4)^3 = c^{12} : c^{4\cdot3} = c^{12} : c^{12} = c^{12-12} = c^0 = 1$$ б) $$(c^2)^9 : (c^2)^8 = c^{2\cdot9} : c^{2\cdot8} = c^{18} : c^{16} = c^{18-16} = c^2$$ в) $$(c^3 \cdot c)^4 : (c^4 \cdot c)^3 = (c^{3+1})^4 : (c^{4+1})^3 = (c^4)^4 : (c^5)^3 = c^{4\cdot4} : c^{5\cdot3} = c^{16} : c^{15} = c^{16-15} = c^1 = c$$