다음을 풀어보세요: 5000*((1+609%)^10-1/609%)

$$5000 \times ( \frac { ( 1 + 609 \% ) ^ { 10 } - 1 } { 609 \% } )$$

계산

$$\frac{52704179649452190345924889}{200000000000000}\approx 263520898247.26095173$$

해답 단계

1과(와) \frac{609}{100}을(를) 더하여 \frac{709}{100}을(를) 구합니다.

$$5000\times \frac{\left(\frac{709}{100}\right)^{10}-1}{\frac{609}{100}}$$

\frac{709}{100}의 10제곱을 계산하여 \frac{32096845506516383920668257401}{100000000000000000000}을(를) 구합니다.

$$5000\times \frac{\frac{32096845506516383920668257401}{100000000000000000000}-1}{\frac{609}{100}}$$

\frac{32096845506516383920668257401}{100000000000000000000}에서 1을(를) 빼고 \frac{32096845406516383920668257401}{100000000000000000000}을(를) 구합니다.

$$5000\times \frac{\frac{32096845406516383920668257401}{100000000000000000000}}{\frac{609}{100}}$$

\frac{32096845406516383920668257401}{100000000000000000000}에 \frac{609}{100}의 역수를 곱하여 \frac{32096845406516383920668257401}{100000000000000000000}을(를) \frac{609}{100}(으)로 나눕니다.

$$5000\times \frac{32096845406516383920668257401}{100000000000000000000}\times \frac{100}{609}$$

\frac{32096845406516383920668257401}{100000000000000000000}과(와) \frac{100}{609}을(를) 곱하여 \frac{52704179649452190345924889}{1000000000000000000}(을)를 구합니다.

$$5000\times \frac{52704179649452190345924889}{1000000000000000000}$$

5000과(와) \frac{52704179649452190345924889}{1000000000000000000}을(를) 곱하여 \frac{52704179649452190345924889}{200000000000000}(을)를 구합니다.

$$\frac{52704179649452190345924889}{200000000000000}$$

인수 분해

$$\frac{11 \cdot 311 \cdot 401 \cdot 809 \cdot 66688751 \cdot 712109051}{2 ^ {15} \cdot 5 ^ {14}} = 263520898247\frac{52196937859072}{200000000000000} = 263520898247.261$$