Найдите значение выражения: а) -0,5¹⁰√1024; б) -2/3 ⁷√-2187; в) 1,5⁹√512; г) ⁵√7 19/32 ⋅ √5 4/9; д) ³√-125 ⋅⁷√0,1⁷; е) ⁴√16^-2 ⋅ ³√0,125³

Решение:

а) -0,5¹⁰√1024

-0,5¹⁰√1024 = -0,5 ⋅ ¹⁰√1024 = -0,5 ⋅ 2 = -1

б) -2/3 ⁷√-2187

-2/3 ⁷√-2187 = 2/3 ⁷√2187 = 2/3 ⁷√3⁷ = 2/3 ⋅ 3 = 2

в) 1,5⁹√512

1,5⁹√512 = 1,5⁹√2⁹ = 1,5 ⋅ 2 – 3

г) ⁵√7 19/32 ⋅ √5 4/9

⁵√7 19/32 ⋅ √5 4/9 = ⁵√243/32 ⋅ √49/9 = 5√(2/3)⁵ ⋅ 7/3 = 3 ⋅ 7 / 2 ⋅ 3 = 7/2

д) ³√-125 ⋅⁷√0,1⁷

³√-125 ⋅⁷√0,1⁷ = -3√5³ ⋅ 0,1 = -5 ⋅ 0,1 = – 0,5

е) ⁴√16^-2 ⋅ ³√0,125³

⁴√16^-2 ⋅ ³√0,125³ = 4√1/16² ⋅ ³ √0,125³ = ⁴ √(1/4)⁴ ⋅ 1/8 = 1/4⋅8 = 1/32

Источник : Учебник по Алгебре 9 класса авторов Ю.Н. Макарычев, Н.Г. Миндюк, К.И. Нешков, С.Б. Суворова, 2014г.