Question
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Іредставьте степень в виде произведения вычислите: \( 6^{4} \); б) \( 11^{3} \); в) \( 28^{3} ; \) г) \( 543^{2} ; \) д) \( 10^{4} \); е) \( 1^{10} \).

Ask by Carroll Fitzgerald. in Turkmenistan
Jan 15,2025

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Answer

\( 6^{4} = 1296 \); \( 11^{3} = 1331 \); \( 28^{3} = 21\,952 \); \( 543^{2} = 294\,849 \); \( 10^{4} = 10\,000 \); \( 1^{10} = 1 \).

Solution

Конвертируем степени в виде произведения и вычисляем их: **а) \( 6^{4} \)** \[ 6^{4} = 6 \times 6 \times 6 \times 6 \] Вычисление: \[ 6 \times 6 = 36 \\ 36 \times 6 = 216 \\ 216 \times 6 = 1296 \\ \] **Ответ:** \( 6^{4} = 1296 \) **б) \( 11^{3} \)** \[ 11^{3} = 11 \times 11 \times 11 \] Вычисление: \[ 11 \times 11 = 121 \\ 121 \times 11 = 1331 \\ \] **Ответ:** \( 11^{3} = 1331 \) **в) \( 28^{3} \)** \[ 28^{3} = 28 \times 28 \times 28 \] Вычисление: \[ 28 \times 28 = 784 \\ 784 \times 28 = 21\,952 \\ \] **Ответ:** \( 28^{3} = 21\,952 \) **г) \( 543^{2} \)** \[ 543^{2} = 543 \times 543 \] Вычисление: \[ 543 \times 500 = 271\,500 \\ 543 \times 40 = 21\,720 \\ 543 \times 3 = 1\,629 \\ 271\,500 + 21\,720 = 293\,220 \\ 293\,220 + 1\,629 = 294\,849 \\ \] **Ответ:** \( 543^{2} = 294\,849 \) **д) \( 10^{4} \)** \[ 10^{4} = 10 \times 10 \times 10 \times 10 \] Вычисление: \[ 10 \times 10 = 100 \\ 100 \times 10 = 1\,000 \\ 1\,000 \times 10 = 10\,000 \\ \] **Ответ:** \( 10^{4} = 10\,000 \) **е) \( 1^{10} \)** \[ 1^{10} = 1 \times 1 \times \ldots \times 1 \ (\text{10 раз}) \] Вычисление: \[ 1^{10} = 1 \\ \] **Ответ:** \( 1^{10} = 1 \)

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Чтобы представить степени в виде произведения, можно записать их в следующем виде: a) \( 6^{4} = 6 \times 6 \times 6 \times 6 = 1296 \) б) \( 11^{3} = 11 \times 11 \times 11 = 1331 \) в) \( 28^{3} = 28 \times 28 \times 28 = 21952 \) г) \( 543^{2} = 543 \times 543 = 294249 \) д) \( 10^{4} = 10 \times 10 \times 10 \times 10 = 10000 \) е) \( 1^{10} = 1 \times 1 \times 1 \times 1 \times 1 \times 1 \times 1 \times 1 \times 1 \times 1 = 1 \) Как видите, степени можно удобно преобразовать в произведение, а потом посчитать, что порой бывает довольно интересно!

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