다음을 풀어보세요: 11001.0225^12-1/0.0225

$$1100 \frac{ { 1.0225 }^{ 12 } -1 }{ 0.0225 }$$

계산

$$14962.443950058887987823224707839488983154296875$$

해답 단계

1.0225의 12제곱을 계산하여 1.306049989887568163387293232660353183746337890625을(를) 구합니다.

$$1100\times \frac{1.306049989887568163387293232660353183746337890625-1}{0.0225}$$

1.306049989887568163387293232660353183746337890625에서 1을(를) 빼고 0.306049989887568163387293232660353183746337890625을(를) 구합니다.

$$1100\times \frac{0.306049989887568163387293232660353183746337890625}{0.0225}$$

분자와 분모 모두에 1000000000000000000000000000000000000000000000000을(를) 곱하여 \frac{0.306049989887568163387293232660353183746337890625}{0.0225}을(를) 확장합니다.

$$1100\times \frac{306049989887568163387293232660353183746337890625}{22500000000000000000000000000000000000000000000}$$

536441802978515625을(를) 추출 및 상쇄하여 분수 \frac{306049989887568163387293232660353183746337890625}{22500000000000000000000000000000000000000000000}을(를) 기약 분수로 약분합니다.

$$1100\times \frac{570518531904616310207990024409}{41943040000000000000000000000}$$

1100\times \frac{570518531904616310207990024409}{41943040000000000000000000000}을(를) 단일 분수로 표현합니다.

$$\frac{1100\times 570518531904616310207990024409}{41943040000000000000000000000}$$

1100과(와) 570518531904616310207990024409을(를) 곱하여 627570385095077941228789026849900(을)를 구합니다.

$$\frac{627570385095077941228789026849900}{41943040000000000000000000000}$$

100을(를) 추출 및 상쇄하여 분수 \frac{627570385095077941228789026849900}{41943040000000000000000000000}을(를) 기약 분수로 약분합니다.

$$\frac{6275703850950779412287890268499}{419430400000000000000000000}$$

인수 분해

$$\frac{3 \cdot 7 \cdot 11 \cdot 13 \cdot 61 \cdot 67 \cdot 293 \cdot 349 \cdot 809 \cdot 1117 \cdot 163627 \cdot 33818377}{2 ^ {42} \cdot 5 ^ {20}} = 14962\frac{1.862061507788246 \times 10^{26}}{4.194304 \times 10^{26}} = 14962.443950058887$$