Вычислите: _ 16^-2*(-10)^-3/128^-4*32^4

Для вычисления данного выражения сначала приведем все числа к основе 2:

16^-2 = (2^4)^-2 = 2^(-8) (-10)^-3 = (-25)^-3 = -2^-3 5^-3 = -1/8 * 1/125 = -1/1000 128^-4 = (2^7)^-4 = 2^(-28) 32^4 = (2^5)^4 = 2^20

Теперь заменим в исходном выражении:

2^(-8) -1/1000 / 2^(-28) 2^20 = 2^(-8) (-1/1000) 2^(20) 2^(28) = 2^(-8 + 20 + 28) (-1/1000) = 2^40 (-1/1000) = 1099511627776 (-1/1000) = -1099511627776 / 1000 = -1099511627.776

Ответ: -1099511627.776.

Чтобы вычислить выражение ( 16^{-2} \times (-10)^{-3} / 128^{-4} \times 32^4 ), следует проделать несколько шагов с использованием свойств степеней.

1. Разложим основания на простые множители:

   • ( 16 = 2^4 )
   • ( -10 = -1 \times 2 \times 5 )
   • ( 128 = 2^7 )
   • ( 32 = 2^5 )

2. Перепишем выражение с учетом разложения на простые множители:

   [ 16^{-2} = (2^4)^{-2} = 2^{-8} ]

   [ (-10)^{-3} = (-1)^{-3} \times (2 \times 5)^{-3} = -1 \times 2^{-3} \times 5^{-3} ]

   [ 128^{-4} = (2^7)^{-4} = 2^{-28} ]

   [ 32^4 = (2^5)^4 = 2^{20} ]

3. Подставим в выражение:

   [ 2^{-8} \times (-1) \times 2^{-3} \times 5^{-3} / 2^{-28} \times 2^{20} ]

4. Объединим степени двойки и пятерки:

   [ (-1) \times 2^{-8-3-20+28} \times 5^{-3} ]

   [ = (-1) \times 2^{-3} \times 5^{-3} ]

5. Упростим выражение:

   [ = - \frac{1}{2^3 \times 5^3} ]

6. Рассчитаем числовое значение:

   [ 2^3 = 8 ]

   [ 5^3 = 125 ]

   [ 2^3 \times 5^3 = 8 \times 125 = 1000 ]

   [ = - \frac{1}{1000} ]

Таким образом, значение выражения равно (-\frac{1}{1000}).

16^-2(-10)^-3/128^-432^4 = 16^-2 (-10)^-3 / 128^-4 32^4 = 1/16^2 -1/10^3 / 1/128^4 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 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1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 -1/1000 / 1/65536 32^4 = 1/256 * -