다음을 풀어보세요: 347*10^22div667*10^-11div6*10^24*15*10^11*15*{10}^11

$$347 \times { 10 }^{ 22 } \div 667 \times { 10 }^{ -11 } \div 6 \times { 10 }^{ 24 } \times 15 \times { 10 }^{ 11 } \times 15 \times { 10 }^{ 11 }$$

계산

$$\frac{13012500000000000000000000000000000000000000000000000000000000}{667}\approx 1.95089955 \cdot 10^{58}$$

해답 단계

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

$$\frac{\frac{347\times 10^{22}}{667}\times 10^{-11}}{6}\times 10^{35}\times 15\times 15\times 10^{11}$$

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

$$\frac{\frac{347\times 10^{22}}{667}\times 10^{-11}}{6}\times 10^{46}\times 15\times 15$$

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

$$\frac{\frac{347\times 10000000000000000000000}{667}\times 10^{-11}}{6}\times 10^{46}\times 15\times 15$$

347과(와) 10000000000000000000000을(를) 곱하여 3470000000000000000000000(을)를 구합니다.

$$\frac{\frac{3470000000000000000000000}{667}\times 10^{-11}}{6}\times 10^{46}\times 15\times 15$$

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

$$\frac{\frac{3470000000000000000000000}{667}\times \frac{1}{100000000000}}{6}\times 10^{46}\times 15\times 15$$

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

$$\frac{\frac{34700000000000}{667}}{6}\times 10^{46}\times 15\times 15$$

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

$$\frac{34700000000000}{667\times 6}\times 10^{46}\times 15\times 15$$

667과(와) 6을(를) 곱하여 4002(을)를 구합니다.

$$\frac{34700000000000}{4002}\times 10^{46}\times 15\times 15$$

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

$$\frac{17350000000000}{2001}\times 10^{46}\times 15\times 15$$

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

$$\frac{17350000000000}{2001}\times 10000000000000000000000000000000000000000000000\times 15\times 15$$

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

$$\frac{173500000000000000000000000000000000000000000000000000000000}{2001}\times 15\times 15$$

\frac{173500000000000000000000000000000000000000000000000000000000}{2001}과(와) 15을(를) 곱하여 \frac{867500000000000000000000000000000000000000000000000000000000}{667}(을)를 구합니다.

$$\frac{867500000000000000000000000000000000000000000000000000000000}{667}\times 15$$

\frac{867500000000000000000000000000000000000000000000000000000000}{667}과(와) 15을(를) 곱하여 \frac{13012500000000000000000000000000000000000000000000000000000000}{667}(을)를 구합니다.

$$\frac{13012500000000000000000000000000000000000000000000000000000000}{667}$$

인수 분해

$$\frac{2 ^ {56} \cdot 3 \cdot 5 ^ {59} \cdot 347}{23 \cdot 29} = 1.950899550224888 \times 10^{58}\frac{535}{667} = 1.950899550224888 \times 10^{58}$$