Алгебра 7 класс контрольные работы Виленкин ответы – страница 70

а) 8³ ∙ 2⁴/4⁵ = 2³ ˙ ³∙ 2⁴/2² ˙ ⁵ = 2⁹∙ 2⁴/2¹⁰ = 2⁹ ⁺ ⁴/2¹⁰ = 2¹³/2¹⁰ = 2^{13 – 10} = 2³ = 8 б) При х = – 1/2     2 – 7х² = 2 – 7 ∙ (– 1/2)² = 2 – 7 ∙ 1/4 = 2 – 7/4 = 2 – 13/4 = 1/4

(– 0,5a¹⁵b⁴)² ∙ (– 4/7ab⁷) = (– 0,5)²a^{15 ∙ 2}b^{4 ∙ 2} ∙ (– 4/7)ab⁷ = 1/4a³⁰b⁸ ∙ (– 4/7)ab⁷ = 1/4 ∙ (– 4/7)a^{30 + 1}b^{8 + 7} = – 1/7a³¹b¹⁵

а) b³ ∙ b¹³ = b^{3 + 13} = b¹⁶ б) b¹² : b⁴ = b^{12 – 4} = b⁸ в) (b⁶)⁵ = b^{6 ∙ 5} = b³⁰ г) (5b⁷)² = 5² ∙ b^{7 ∙ 2} = 25b¹⁴

а) 3х⁵у ∙ (– 5/3ху⁶) = 3 ∙ (– 5/3) ∙ х^{5 + 1}у^{1 + 6} = – 5х⁶у⁷ б) (– 4x⁴y¹¹)³ = (– 4)³x^{4 ∙ 3}y^{11 ∙ 3} = – 64x¹²y³³

а) у(1,5) = 2,25 б) х² = 5     х = 2,2   х = – 2,2

а) 4¹² ∙ 2⁵/8⁹ = 2² ˙ ¹²∙ 2⁵/2³ ˙ ⁹ = 2²⁴∙ 2⁵/2²⁷ = 2²⁴ ⁺ ⁵/2²⁷ = 2²⁹/2²⁷ = 2^{29 – 27} = 2² = 4 б) При х = – 1/3     5 + 6х³ = 5 + 6 ∙ (– 1/3)³ = 5 – 6 ∙ 1/27 = 5 – 2/9 = 4 7/9

(– 2/3a¹³b⁸)² ∙ (– 5/4a⁴b) = (– 2/3)²a^{13 ∙ 2}b^{8 ∙ 2} ∙ (– 5/4)a⁴b = 4/9a²⁶b¹⁶ ∙ (– 5/4)a⁴b = – 5/9a^{26 + 4}b^{16 + 1} = – 5/9a³⁰b¹⁷

а) с⁶ ∙ с⁹ = с^{6 + 9} = с¹⁵ б) с²¹ : с⁷ = с^{21 – 7} = с¹⁴ в) (с⁹)⁸ = с^{9 ∙ 8} = с⁷² г) (4с⁵)³ = 4³ ∙ с^{5 ∙ 3} = 64с¹⁵

а) – 8a⁴b¹² ∙ 2,5ab³ = – 8 ∙ 2,5 ∙ a^{4 + 1}b^{12 + 3} = – 20a⁵b¹⁵ б) (– 5a²b⁶)⁴ = (– 5)⁴a^{2 ∙ 4}b^{6 ∙ 4} = 625a⁸b²⁴