ГДЗ по Алгебре 7 Класс Номер 575 Дорофеев, Суворова — Подробные Ответы

а) \(3x \cdot (2x)^3\)

б) \(4b \cdot (3b)^2\)

в) \(-2a \cdot (ab^2)^2\)

г) \((x^2y)^3 \cdot (-x)\)

д) \(2y \cdot (-4y)^2\)

е) \((-b)^3 \cdot 5ab\)

ж) \(-x \cdot (x^2y)^4\)

з) \(10a \cdot (10a)^3\)

и) \((-2m^3)^2 \cdot 5mn\)

а) \(3x \cdot (2x)^3 = 3x \cdot 8x^3 = 24x^4\)

б) \(4b \cdot (3b)^3 = 4b \cdot 27b^3 = 108b^4\)

в) \(-2a \cdot (ab^2)^2 = -2a \cdot a^2b^4 = -2a^3b^4\)

г) \((x^2y)^3 \cdot (-x) = x^6y^3 \cdot (-x) = -x^7y^3\)

д) \(2y \cdot (-4y)^2 = 2y \cdot 16y^2 = 32y^3\)

е) \((-b)^3 \cdot 5ab = -b^3 \cdot 5ab = -5ab^4\)

ж) \(-x \cdot (x^2y)^4 = -x \cdot x^8y^4 = -x^9y^4\)

з) \(10a \cdot (10a)^3 = 10a \cdot 1000a^3 = 10\,000a^4\)

и) \((-2m^3)^2 \cdot 5mn = 4m^6 \cdot 5mn = 20m^7n\)

а) \(3x \cdot (2x)^3 = 3x \cdot (2^3 \cdot x^3) = 3x \cdot 8x^3 = 3 \cdot 8 \cdot x \cdot x^3 = 24x^{1+3} = 24x^4\)

б) \(4b \cdot (3b)^3 = 4b \cdot (3^3 \cdot b^3) = 4b \cdot 27b^3 = 4 \cdot 27 \cdot b \cdot b^3 = 108b^{1+3} = 108b^4\)

в) \(-2a \cdot (ab^2)^2 = -2a \cdot (a^2 \cdot b^{2 \cdot 2}) = -2a \cdot a^2b^4 = -2 \cdot a \cdot a^2 \cdot b^4 = -2a^{1+2}b^4 = -2a^3b^4\)

г) \((x^2y)^3 \cdot (-x) = (x^{2 \cdot 3} \cdot y^3) \cdot (-x) = (x^6y^3) \cdot (-x) = -x^6y^3 \cdot x = -x^{6+1}y^3 = -x^7y^3\)

д) \(2y \cdot (-4y)^2 = 2y \cdot ((-4)^2 \cdot y^2) = 2y \cdot 16y^2 = 2 \cdot 16 \cdot y \cdot y^2 = 32y^{1+2} = 32y^3\)

е) \((-b)^3 \cdot 5ab = (-1)^3 \cdot b^3 \cdot 5ab = -b^3 \cdot 5ab = -5ab \cdot b^3 = -5a b^{1+3} = -5ab^4\)

ж) \(-x \cdot (x^2y)^4 = -x \cdot (x^{2 \cdot 4} \cdot y^4) = -x \cdot x^8y^4 = -x^1 x^8 y^4 = -x^{1+8}y^4 = -x^9y^4\)

з) \(10a \cdot (10a)^3 = 10a \cdot (10^3 \cdot a^3) = 10a \cdot 1000a^3 = 10 \cdot 1000 \cdot a \cdot a^3 = 10000 a^{1+3} = 10000a^4\)

и) \((-2m^3)^2 \cdot 5mn = ((-2)^2 \cdot (m^3)^2) \cdot 5mn = 4 \cdot m^{3 \cdot 2} \cdot 5mn = 4m^6 \cdot 5mn = 4 \cdot 5 \cdot m^6 \cdot m \cdot n = 20 m^{6+1} n = 20m^7 n\)