1. Упростите выражение: 1) a) x³. (-x⁴); б) x³· (-x)²; в) (-x³)³· x⁴; г) (-x³)· (-x)⁴; 2) a) (a²)⁵·a⁵; б) (a²·a⁵)²; в) a⁴·(a⁴)⁴; г) (a·a⁷)²; 3) a) (c⁴)²·(c²)⁴; б) (c·c²)²·(c·c²)³; в) (c⁵)²·(c²·c³)²; 4) a) y¹²: (y⁶)²; б) (y⁴)⁵: (y⁴)²; в) (y·y²)³ : (y·y³)².

Ответ:

1) a) \(x^3 \cdot (-x^4) = -x^{3+4} = -x^7\) б) \(x^3 \cdot (-x)^2 = x^3 \cdot x^2 = x^{3+2} = x^5\) в) \((-x^3)^3 \cdot x^4 = (-1)^3 \cdot x^{3\cdot3} \cdot x^4 = -x^9 \cdot x^4 = -x^{9+4} = -x^{13}\) г) \((-x^3) \cdot (-x)^4 = (-x^3) \cdot x^4 = -x^{3+4} = -x^7\) 2) a) \((a^2)^5 \cdot a^5 = a^{2\cdot5} \cdot a^5 = a^{10} \cdot a^5 = a^{10+5} = a^{15}\) б) \((a^2 \cdot a^5)^2 = (a^{2+5})^2 = (a^7)^2 = a^{7\cdot2} = a^{14}\) в) \(a^4 \cdot (a^4)^4 = a^4 \cdot a^{4\cdot4} = a^4 \cdot a^{16} = a^{4+16} = a^{20}\) г) \((a \cdot a^7)^2 = (a^{1+7})^2 = (a^8)^2 = a^{8\cdot2} = a^{16}\) 3) a) \((c^4)^2 \cdot (c^2)^4 = c^{4\cdot2} \cdot c^{2\cdot4} = c^8 \cdot c^8 = c^{8+8} = c^{16}\) б) \((c \cdot c^2)^2 \cdot (c \cdot c^2)^3 = (c^{1+2})^2 \cdot (c^{1+2})^3 = (c^3)^2 \cdot (c^3)^3 = c^{3\cdot2} \cdot c^{3\cdot3} = c^6 \cdot c^9 = c^{6+9} = c^{15}\) в) \((c^5)^2 \cdot (c^2 \cdot c^3)^2 = c^{5\cdot2} \cdot (c^{2+3})^2 = c^{10} \cdot (c^5)^2 = c^{10} \cdot c^{5\cdot2} = c^{10} \cdot c^{10} = c^{10+10} = c^{20}\) 4) a) \(y^{12} : (y^6)^2 = y^{12} : y^{6\cdot2} = y^{12} : y^{12} = y^{12-12} = y^0 = 1\) б) \((y^4)^5 : (y^4)^2 = y^{4\cdot5} : y^{4\cdot2} = y^{20} : y^8 = y^{20-8} = y^{12}\) в) \((y \cdot y^2)^3 : (y \cdot y^3)^2 = (y^{1+2})^3 : (y^{1+3})^2 = (y^3)^3 : (y^4)^2 = y^{3\cdot3} : y^{4\cdot2} = y^9 : y^8 = y^{9-8} = y^1 = y\)