다음을 풀어보세요: left(3546+10^-5right)^9/left(505*10^2right)^12

$$\frac{ { \left(3546+ { 10 }^{ -5 } \right) }^{ 9 } }{ { \left(505 \times { 10 }^{ 2 } \right) }^{ 12 } }$$

계산

$$\frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{275103767122062920083301025390625000000000000000000000000000000000000000000000000000000000000000000000}\approx 3.222196748 \cdot 10^{-25}$$

해답 단계

10의 -5제곱을 계산하여 \frac{1}{100000}을(를) 구합니다.

$$\frac{\left(3546+\frac{1}{100000}\right)^{9}}{\left(505\times 10^{2}\right)^{12}}$$

3546과(와) \frac{1}{100000}을(를) 더하여 \frac{354600001}{100000}을(를) 구합니다.

$$\frac{\left(\frac{354600001}{100000}\right)^{9}}{\left(505\times 10^{2}\right)^{12}}$$

\frac{354600001}{100000}의 9제곱을 계산하여 \frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{1000000000000000000000000000000000000000000000}을(를) 구합니다.

$$\frac{\frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{1000000000000000000000000000000000000000000000}}{\left(505\times 10^{2}\right)^{12}}$$

10의 2제곱을 계산하여 100을(를) 구합니다.

$$\frac{\frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{1000000000000000000000000000000000000000000000}}{\left(505\times 100\right)^{12}}$$

505과(와) 100을(를) 곱하여 50500(을)를 구합니다.

$$\frac{\frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{1000000000000000000000000000000000000000000000}}{50500^{12}}$$

50500의 12제곱을 계산하여 275103767122062920083301025390625000000000000000000000000을(를) 구합니다.

$$\frac{\frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{1000000000000000000000000000000000000000000000}}{275103767122062920083301025390625000000000000000000000000}$$

\frac{\frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{1000000000000000000000000000000000000000000000}}{275103767122062920083301025390625000000000000000000000000}을(를) 단일 분수로 표현합니다.

$$\frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{1000000000000000000000000000000000000000000000\times 275103767122062920083301025390625000000000000000000000000}$$

1000000000000000000000000000000000000000000000과(와) 275103767122062920083301025390625000000000000000000000000을(를) 곱하여 275103767122062920083301025390625000000000000000000000000000000000000000000000000000000000000000000000(을)를 구합니다.

$$\frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{275103767122062920083301025390625000000000000000000000000000000000000000000000000000000000000000000000}$$