1. а) \(x^3 \cdot (-x^4) = -x^{3+4} = -x^7\); б) \(x^3 \cdot (-x^4) = -x^{3+4} = -x^7\); в) \((-x)^3 \cdot x^4 = -x^{3+4} = -x^7\); г) \((-x^3) \cdot (-x^4) = x^{3+4} = x^7\).
2. а) \((a^2)^5 \cdot a^5 = a^{2 \cdot 5} \cdot a^5 = a^{10+5} = a^{15}\); б) \((a^2 \cdot a^5)^2 = (a^{2+5})^2 = a^{7 \cdot 2} = a^{14}\); в) \(a^4 \cdot (a^4)^4 = a^4 \cdot a^{4 \cdot 4} = a^4 \cdot a^{16} = a^{4+16} = a^{20}\); г) \((a \cdot a^7)^7 = a^{1+7}^7 = a^{8 \cdot 7} = a^{56}\).
3. а) \((c^4)^2 \cdot (c^2)^4 = c^{4 \cdot 2} \cdot c^{2 \cdot 4} = c^8 \cdot c^8 = c^{8+8} = c^{16}\); б) \((c \cdot c^2)^2 \cdot (c \cdot c^2)^3 = c^{1+2}^2 \cdot c^{1+2}^3 = c^3 \cdot c^6 = c^{3+6} = c^9\); в) \((c^5)^2 \cdot (c^2 \cdot c^3)^2 = c^{5 \cdot 2} \cdot c^{2+3}^2 = c^{10} \cdot c^{10} = c^{10+10} = c^{20}\).
4. а) \(u^{12} \cdot (u^6)^2 = u^{12} \cdot u^{6 \cdot 2} = u^{12} \cdot u^{12} = u^{12+12} = u^{24}\); б) \((u^4)^5 \cdot (u^4)^2 = u^{4 \cdot 5} \cdot u^{4 \cdot 2} = u^{20} \cdot u^{8} = u^{20+8} = u^{28}\); в) \((u \cdot u^2)^3 \cdot (u \cdot u^3)^2 = u^{1+2}^3 \cdot u^{1+3}^2 = u^{9} \cdot u^{8} = u^{9+8} = u^{17}\).
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