Вопрос:

№2. Упростите 1) (x^7)^3 : (x^5)^4

№2. Упростите
1) (x^7)^3 : (x^5)^4
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Ответ ассистента

№2. Упростите: 1) $(x^7)^3 : (x^5)^4 = x^{21} : x^{20} = x^{21-20} = x^1 = x$ 2) $(x^6)^3 \times (x^3)^5 = x^{18} \times x^{15} = x^{18+15} = x^{33}$ 3) $(x^6 : x^1) : x^2 = x^{6-1} : x^2 = x^5 : x^2 = x^{5-2} = x^3$ 4) $(x^5 : x^0) : x^3 = x^{5-0} : x^3 = x^5 : x^3 = x^{5-3} = x^2$ 5) $(x^4)^7 : x^0 : x^5 = x^{28} : 1 : x^5 = x^{28-5} = x^{23}$ 6) $((x^4)^5 \times x^8) : x^6 = (x^{20} \times x^8) : x^6 = x^{28} : x^6 = x^{28-6} = x^{22}$ 7) $((x^5)^3 \times (x^4)^2) : x^5 = (x^{15} \times x^8) : x^5 = x^{23} : x^5 = x^{23-5} = x^{18}$ 8) $((x^4)^3 \times (x^5)^3) : x^{10} = (x^{12} \times x^{15}) : x^{10} = x^{27} : x^{10} = x^{17}$ 9) $(x^{17} \times (x^{12})^3) : x^{15} = (x^{17} \times x^{36}) : x^{15} = x^{53} : x^{15} = x^{38}$ 10) $(x^{11})^2 \times x^7 : (x^5)^3 = (x^{22} \times x^7) : x^{15} = x^{29} : x^{15} = x^{14}$ 11) $((x^{24})^3 \times x^5) : ((x^6)^3 \times x^{15}) = (x^{72} \times x^5) : (x^{18} \times x^{15}) = x^{77} : x^{33} = x^{44}$ 12) $((x^9)^8 : (x^5)^7) : ((x^4)^9 : x^{12}) = (x^{72} : x^{35}) : (x^{36} : x^{12}) = x^{37} : x^{24} = x^{13}$ 13) $((x^{12})^5 \times (x^4)^{13}) : ((x^{14})^8 : (x^3)^{16}) = (x^{60} \times x^{52}) : (x^{112} : x^{48}) = x^{112} : x^{64} = x^{48}$ №3. Упростите: 1) $(2^8)^2 : (2^3)^3 = 2^{16} : 2^9 = 2^{16-9} = 2^7 = 128$ 2) $(7^5)^5 \times (7^6)^6 = 7^{25} \times 7^{36} = 7^{25+36} = 7^{61}$ 3) $(0,5)^{12} : (0,5)^3 = (0,5)^{12-3} = (0,5)^9$ 4) $(\frac{4}{7})^{15} \times (\frac{4}{7})^{18} = (\frac{4}{7})^{15+18} = (\frac{4}{7})^{33}$ 5) $(3^{10} \times (3^2)^3) : (3^1 \times (3^5)^2) = (3^{10} \times 3^6) : (3^1 \times 3^{10}) = 3^{16} : 3^{11} = 3^5 = 243$ 6) $(4^7 \times (4^4)^2) : (4^1 \times (4^3)^3) = (4^7 \times 4^8) : (4^1 \times 4^9) = 4^{15} : 4^{10} = 4^5 = 1024$ 7) $((5^4)^5 : (5^2)^4) : (5^1 \times (5^5)^2) = (5^{20} : 5^8) : (5^1 \times 5^{10}) = 5^{12} : 5^{11} = 5^1 = 5$ 8) $((2^3)^4 \times (2^5)^2) : (2^1 \times (2^3)^5) = (2^{12} \times 2^{10}) : (2^1 \times 2^{15}) = 2^{22} : 2^{16} = 2^6 = 64$ 9) $((0,3)^7 \times (0,3)^{22}) : ((0,3)^{21} \times (0,3)^7) = (0,3)^{29} : (0,3)^{28} = (0,3)^1 = 0,3$ 10) $((0,4)^9 \times (0,4)^{18}) : ((0,4)^{21} \times (0,4)^2) = (0,4)^{27} : (0,4)^{23} = (0,4)^4 = 0,0256$

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