ГДЗ по Алгебре 7 Класс Номер 576 Дорофеев, Суворова — Подробные Ответы

а) \((a^2b^2)^2 : (ab^3)^3\)

б) \((x^3y)^3 \cdot (xy^3)^3\)

в) \(\left(-\frac{1}{2}m^2n^3\right)^2 \cdot (4mn^3)^2\)

г) \{(-y^2)^2 \cdot (2y^2)^3 \cdot 0{,}5z\}

д) \{(-0{,}1a^2b^3)^3\}

е) \(-0{,}01c^3(-10ac^2)^2\)

а) \((a^2b^2)^2 : (ab^3)^3 = a^{4}b^{4} : a^3b^6 = a^{4-3}b^{4-6} = a^{1}b^{-2} = \frac{a}{b^2}\)

б) \((x^3y)^3 \cdot (xy^3)^3 = x^{9}y^3 \cdot x^3y^9 = x^{9+3}y^{3+9} = x^{12}y^{12}\)

в) \(\left(-\frac{1}{2}m^2n^3\right)^2 \cdot (4mn^3)^2 = \frac{1}{4}m^4n^6 \cdot 16m^2n^6 = 4m^{4+2}n^{6+6} = 4m^6n^{12}\)

г) \{(-y^2)^2 \cdot (2y^2)^3 \cdot 0{,}5z\} = y^4 \cdot 8y^6 \cdot 0,5z = 8y^{10} \cdot 0,5z = 4y^{10}z\)

д) \{(-0{,}1a^2b^3)^3\} = (-0,1)^3(a^2)^3(b^3)^3 = -0,001 a^6 b^9\)

е) \(-0{,}01c^3(-10ac^2)^2 = -0,01c^3 \cdot 100 a^2 c^4 = -a^2 c^{3+4} = -a^2 c^7\)

а) \((a^2b^2)^2 : (ab^3)^3 = (a^2)^2 \cdot (b^2)^2 : (a^1)^3 \cdot (b^3)^3 = a^{2\cdot2}b^{2\cdot2} : a^{1\cdot3}b^{3\cdot3} = a^4b^4 : a^3b^9 = \frac{a^4b^4}{a^3b^9} = a^{4-3}b^{4-9} = a^1b^{-5} = \frac{a}{b^5}\)

б) \((x^3y)^3 \cdot (xy^3)^3 = (x^3)^3(y)^3 \cdot (x)^3(y^3)^3 = x^{3\cdot3}y^3 \cdot x^3y^{3\cdot3} = x^9y^3 \cdot x^3y^9 = x^{9+3}y^{3+9} = x^{12}y^{12}\)

в) \(\left(-\frac{1}{2}m^2n^3\right)^2 \cdot (4mn^3)^2 = \left(-\frac{1}{2}\right)^2(m^2)^2(n^3)^2 \cdot (4)^2(m)^2(n^3)^2 = \frac{1}{4}m^4n^6 \cdot 16m^2n^6 = \frac{1}{4}\cdot16 \cdot m^{4+2} n^{6+6} = 4m^6 n^{12}\)

г) \{(-y^2)^2 \cdot (2y^2)^3 \cdot 0{,}5z\} = (-1)^2(y^2)^2 \cdot 2^3(y^2)^3 \cdot 0{,}5z = 1 \cdot y^{2\cdot2} \cdot 8 y^{2\cdot3} \cdot 0{,}5z = y^4 \cdot 8y^6 \cdot 0{,}5z = (y^4 \cdot y^6) \cdot (8\cdot0,5)z = y^{4+6} \cdot 4z = y^{10} \cdot 4z = 4y^{10}z\)

д) \{(-0{,}1a^2b^3)^3\} = (-0,1)^3 (a^2)^3 (b^3)^3 = (-1)^3 \cdot (0,1)^3 \cdot a^{2\cdot3} \cdot b^{3\cdot3} = -1 \cdot 0,001 \cdot a^6 b^9 = -0,001 a^6 b^9\)

е) \(-0{,}01c^3(-10ac^2)^2 = -0,01c^3 \cdot ((-10)^2 \cdot a^2 \cdot (c^2)^2) = -0,01c^3 \cdot 100 a^2 c^4 = -0,01 \cdot 100 \cdot a^2 \cdot c^{3+4} = -1 \cdot a^2 c^7 = -a^2c^7\)