Вопрос
((1)/(5))^3 cdot((1)/(5))^2 cdot((1)/(25))^-4
Решения
4.2
(197 Голоса)
Ульяна
Экспертная проверка
элита · Репетитор 8 лет
Ответ
To solve the expression \( \left(\frac{1}{5}\right)^{3} \cdot\left(\frac{1}{5}\right)^{2} \cdot\left(\frac{1}{25}\right)^{-4} \), we can use the properties of exponents.First, let's simplify each term separately:1. \( \left(\frac{1}{5}\right)^{3} = \frac{1}{5^3} = \frac{1}{125} \)2. \( \left(\frac{1}{5}\right)^{2} = \frac{1}{5^2} = \frac{1}{25} \)3. \( \left(\frac{1}{25}\right)^{-4} = \left(25\right)^{4} = 25^4 = 390625 \)Now, we can multiply these simplified terms together:
To multiply fractions, we multiply the numerators together and the denominators together:
Finally, we can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 625:
Therefore, the correct answer is
.