다음을 풀어보세요: frac{9*10^{8}*(16*10^{-19})^2}{667*10^-11*91*10^-31*166*10^-27}

$$\frac { 9 \times 10 ^ { 8 } \times ( 16 \times 10 ^ { - 19 } ) ^ { 2 } } { 667 \times 10 ^ { - 11 } \times 91 \times 10 ^ { - 31 } \times 166 \times 10 ^ { - 27 } }$$

계산

$$\frac{1152000000000000000000000000000000000000000}{5037851}\approx 2.286689305 \cdot 10^{35}$$

해답 단계

같은 기수의 제곱을 곱하려면 해당 지수를 더합니다. -11과(와) -31을(를) 더하여 -42을(를) 구합니다.

$$\frac{9\times 10^{8}\times \left(16\times 10^{-19}\right)^{2}}{667\times 10^{-42}\times 91\times 166\times 10^{-27}}$$

같은 기수의 제곱을 곱하려면 해당 지수를 더합니다. -42과(와) -27을(를) 더하여 -69을(를) 구합니다.

$$\frac{9\times 10^{8}\times \left(16\times 10^{-19}\right)^{2}}{667\times 10^{-69}\times 91\times 166}$$

동일한 기수의 제곱을 나누려면 분모의 지수를 분자의 지수에서 뺍니다.

$$\frac{9\times 10^{77}\times \left(16\times 10^{-19}\right)^{2}}{91\times 166\times 667}$$

10의 77제곱을 계산하여 100000000000000000000000000000000000000000000000000000000000000000000000000000을(를) 구합니다.

$$\frac{9\times 100000000000000000000000000000000000000000000000000000000000000000000000000000\times \left(16\times 10^{-19}\right)^{2}}{91\times 166\times 667}$$

9과(와) 100000000000000000000000000000000000000000000000000000000000000000000000000000을(를) 곱하여 900000000000000000000000000000000000000000000000000000000000000000000000000000(을)를 구합니다.

$$\frac{900000000000000000000000000000000000000000000000000000000000000000000000000000\times \left(16\times 10^{-19}\right)^{2}}{91\times 166\times 667}$$

10의 -19제곱을 계산하여 \frac{1}{10000000000000000000}을(를) 구합니다.

$$\frac{900000000000000000000000000000000000000000000000000000000000000000000000000000\times \left(16\times \frac{1}{10000000000000000000}\right)^{2}}{91\times 166\times 667}$$

16과(와) \frac{1}{10000000000000000000}을(를) 곱하여 \frac{1}{625000000000000000}(을)를 구합니다.

$$\frac{900000000000000000000000000000000000000000000000000000000000000000000000000000\times \left(\frac{1}{625000000000000000}\right)^{2}}{91\times 166\times 667}$$

\frac{1}{625000000000000000}의 2제곱을 계산하여 \frac{1}{390625000000000000000000000000000000}을(를) 구합니다.

$$\frac{900000000000000000000000000000000000000000000000000000000000000000000000000000\times \frac{1}{390625000000000000000000000000000000}}{91\times 166\times 667}$$

900000000000000000000000000000000000000000000000000000000000000000000000000000과(와) \frac{1}{390625000000000000000000000000000000}을(를) 곱하여 2304000000000000000000000000000000000000000(을)를 구합니다.

$$\frac{2304000000000000000000000000000000000000000}{91\times 166\times 667}$$

91과(와) 166을(를) 곱하여 15106(을)를 구합니다.

$$\frac{2304000000000000000000000000000000000000000}{15106\times 667}$$

15106과(와) 667을(를) 곱하여 10075702(을)를 구합니다.

$$\frac{2304000000000000000000000000000000000000000}{10075702}$$

2을(를) 추출 및 상쇄하여 분수 \frac{2304000000000000000000000000000000000000000}{10075702}을(를) 기약 분수로 약분합니다.

$$\frac{1152000000000000000000000000000000000000000}{5037851}$$

인수 분해

$$\frac{2 ^ {46} \cdot 3 ^ {2} \cdot 5 ^ {39}}{7 \cdot 13 \cdot 23 \cdot 29 \cdot 83} = 2.2866893046261194 \times 10^{35}\frac{336198}{5037851} = 2.2866893046261194 \times 10^{35}$$