다음을 풀어보세요: 3.47*10^22div6.67*10^-11div6*10^24*1.5*10^11*1.5*{10}^11

$$3.47 \times { 10 }^{ 22 } \div 6.67 \times { 10 }^{ -11 } \div 6 \times { 10 }^{ 24 } \times 1.5 \times { 10 }^{ 11 } \times 1.5 \times { 10 }^{ 11 }$$

계산

$$\frac{130125000000000000000000000000000000000000000000000000000000}{667}\approx 1.95089955 \cdot 10^{56}$$

해답 단계

같은 기수의 제곱을 곱하려면 해당 지수를 더합니다. 24과(와) 11을(를) 더하여 35을(를) 구합니다.

$$\frac{\frac{3.47\times 10^{22}}{6.67}\times 10^{-11}}{6}\times 10^{35}\times 1.5\times 1.5\times 10^{11}$$

같은 기수의 제곱을 곱하려면 해당 지수를 더합니다. 35과(와) 11을(를) 더하여 46을(를) 구합니다.

$$\frac{\frac{3.47\times 10^{22}}{6.67}\times 10^{-11}}{6}\times 10^{46}\times 1.5\times 1.5$$

10의 22제곱을 계산하여 10000000000000000000000을(를) 구합니다.

$$\frac{\frac{3.47\times 10000000000000000000000}{6.67}\times 10^{-11}}{6}\times 10^{46}\times 1.5\times 1.5$$

3.47과(와) 10000000000000000000000을(를) 곱하여 34700000000000000000000(을)를 구합니다.

$$\frac{\frac{34700000000000000000000}{6.67}\times 10^{-11}}{6}\times 10^{46}\times 1.5\times 1.5$$

분자와 분모 모두에 100을(를) 곱하여 \frac{34700000000000000000000}{6.67}을(를) 확장합니다.

$$\frac{\frac{3470000000000000000000000}{667}\times 10^{-11}}{6}\times 10^{46}\times 1.5\times 1.5$$

10의 -11제곱을 계산하여 \frac{1}{100000000000}을(를) 구합니다.

$$\frac{\frac{3470000000000000000000000}{667}\times \frac{1}{100000000000}}{6}\times 10^{46}\times 1.5\times 1.5$$

\frac{3470000000000000000000000}{667}과(와) \frac{1}{100000000000}을(를) 곱하여 \frac{34700000000000}{667}(을)를 구합니다.

$$\frac{\frac{34700000000000}{667}}{6}\times 10^{46}\times 1.5\times 1.5$$

\frac{\frac{34700000000000}{667}}{6}을(를) 단일 분수로 표현합니다.

$$\frac{34700000000000}{667\times 6}\times 10^{46}\times 1.5\times 1.5$$

667과(와) 6을(를) 곱하여 4002(을)를 구합니다.

$$\frac{34700000000000}{4002}\times 10^{46}\times 1.5\times 1.5$$

2을(를) 추출 및 상쇄하여 분수 \frac{34700000000000}{4002}을(를) 기약 분수로 약분합니다.

$$\frac{17350000000000}{2001}\times 10^{46}\times 1.5\times 1.5$$

10의 46제곱을 계산하여 10000000000000000000000000000000000000000000000을(를) 구합니다.

$$\frac{17350000000000}{2001}\times 10000000000000000000000000000000000000000000000\times 1.5\times 1.5$$

\frac{17350000000000}{2001}과(와) 10000000000000000000000000000000000000000000000을(를) 곱하여 \frac{173500000000000000000000000000000000000000000000000000000000}{2001}(을)를 구합니다.

$$\frac{173500000000000000000000000000000000000000000000000000000000}{2001}\times 1.5\times 1.5$$

\frac{173500000000000000000000000000000000000000000000000000000000}{2001}과(와) 1.5을(를) 곱하여 \frac{86750000000000000000000000000000000000000000000000000000000}{667}(을)를 구합니다.

$$\frac{86750000000000000000000000000000000000000000000000000000000}{667}\times 1.5$$

\frac{86750000000000000000000000000000000000000000000000000000000}{667}과(와) 1.5을(를) 곱하여 \frac{130125000000000000000000000000000000000000000000000000000000}{667}(을)를 구합니다.

$$\frac{130125000000000000000000000000000000000000000000000000000000}{667}$$

인수 분해

$$\frac{3 \cdot 347 \cdot 2 ^ {54} \cdot 5 ^ {57}}{23 \cdot 29} = 1.9508995502248876 \times 10^{56}\frac{366}{667} = 1.9508995502248876 \times 10^{56}$$