Question

Задание 2. выполнить деление:
a) 5a/4b*25a²/8
b) 3ab/4xy²:(-21ab/10x²)
c) (-6x²/m³n):(-x/3mn²)
задание 3.
выполните действие:
a)2ab/3x*6x²y/4ax²*6a/15b
b)12m²n²/35p*14n²/m³*5mp/21n⁶
c)3x/5y²:9x²/2y:3x/5y
задание 4.
возведите в степень:
a)(x/2a)²
b)(3a²/b)³
c)(2n²/a³)^-²
задание 5.
выполните действия:
a)(8x/a)²*(ab/4x)³
b)(9y/c²)²:(c/3y)^-³
c)(2x²/3y)²:(4x³/3y²)²
задание 6.
выполнить действия:
a)-5x/16a²b*12ab²
b)11a⁴/6b²*5a/6b³:11b³/12a³
c)-3x²/5y³:9x³/2y²*5y/3x
решить..

Answer 1

2.

a) 5a/4b * 25a²/8 =(5a * 25a²)/(4b * 8) = 125a³/32b

b) (3ab/4xy²) : (-21ab/10x²) = 3ab/4xy² * 10x²/-21ab = -(30abx²/84abxy²) = -5x/14y²

c) (-6x²/m³n) : (-x/3mn²) = (-6x²/m³n) * (3mn²/-x) = 18mn²x²/m³nx = 18nx/m²

3.

a) 2ab/3x * 6x²y/4ax² * 6a/15b = 12abx²y/12ax³ * 6a/15b = by/x * 2a/5b = 2aby/5bx = 2ay/5x

b) 12m²n²/35p * 14n²/m³ * 5mp/21n⁶ = 168m²n⁴/35m³p * 5mp/21n⁶ = 24m²n⁴/5m³p * 5mp/21n⁶ = 120m³n⁴p/105m³n⁶p = 8/7n²

c) 3x/5y² : 9x²/2y : 3x/5y = 3x/5y² * 2y/9x² : 3x/5y = 6xy/45x²y² * 5y/3x = 2/15xy * 5y/3x = 10y/45x²y = 10/45x² = 2/9x²

4.

a) (x/2a)² = x/2a * x/2a = x²/4a²

b) (3a²/b)³ = 3a²/b * 3a²/b * 3a²/b = 9a⁴/b² * 3a²/b = 27a⁶/b³

c) $(2n^2/a^3)^{-2}$ = $\frac{1}{2n^2/a^3 * 2n^2/a^3}$ = $\frac{1}{\frac{4n^4}{a^6}}$ = 1 : 4n⁴/a⁶ = 1 * a⁶/4n⁴ = a⁶/4n⁴

5.

a) (8x/a)² * (ab/4x)³ = 64x²/a² * a³b³/64x³ = 64a³b³x²/64x³a² = ab³/x

b) (9y/c²)² : (c/3y$)^{-3}$ = 81y²/c⁴ : 1/(c³/27y³) = 81y²/c⁴ : 27y³/c³ = 81y²/c⁴ * c³/27y³ = 81c³y²/27c⁴y³ = 3/cy

c) (2x²/3y)² : (4x³/3y²)² = 4x⁴/9y² : 16x⁶/9y⁴ = 4x⁴/9y² * 9y⁴/16x⁶ = 36x⁴y⁴/144x⁶y² = 4y²/16x² = y²/4x²

6.

a) -5x/16a²b * 12ab² = -60ab²x/16a²b = -(15b/4a)

b) 11a⁴/6b² * 5a/6b³ : 11b³/12a³ = 55a⁵/36b⁵ * 12a³/11b³ = 660a⁸/396b⁸ = 5a⁸/3b⁸

c) -3x²/5y³ : 9x³/2y² * 5y/3x = -3x²/5y³ * 9x³/2y² * 5y/3x = -27x⁵/10y⁵ * 5y/3x = -(135x⁵y/30y⁵x) = -(45x⁴/10y⁴)