Solve (6.7*10^-11800000000000*5.972*10^24/6371^2)div5.972*10^24

$$(6.7 \times { 10 }^{ -11 } \frac{ 800000000000 \times 5.972 \times { 10 }^{ 24 } }{ { 6371 }^{ 2 } } ) \div 5.972 \times { 10 }^{ 24 }$$

Evaluate

$$\frac{53600000000000000000000000000000000000000000000000}{40589641}\approx 1.320533976 \cdot 10^{42}$$

Solution Steps

Calculate 10 to the power of -11 and get \frac{1}{100000000000}.

$$\frac{6.7\times \frac{1}{100000000000}\times \frac{800000000000\times 5.972\times 10^{24}}{6371^{2}}}{5.972}\times 10^{24}$$

Multiply 6.7 and \frac{1}{100000000000} to get \frac{67}{1000000000000}.

$$\frac{\frac{67}{1000000000000}\times \frac{800000000000\times 5.972\times 10^{24}}{6371^{2}}}{5.972}\times 10^{24}$$

Multiply 800000000000 and 5.972 to get 4777600000000.

$$\frac{\frac{67}{1000000000000}\times \frac{4777600000000\times 10^{24}}{6371^{2}}}{5.972}\times 10^{24}$$

Calculate 10 to the power of 24 and get 1000000000000000000000000.

$$\frac{\frac{67}{1000000000000}\times \frac{4777600000000\times 1000000000000000000000000}{6371^{2}}}{5.972}\times 10^{24}$$

Multiply 4777600000000 and 1000000000000000000000000 to get 4777600000000000000000000000000000000.

$$\frac{\frac{67}{1000000000000}\times \frac{4777600000000000000000000000000000000}{6371^{2}}}{5.972}\times 10^{24}$$

Calculate 6371 to the power of 2 and get 40589641.

$$\frac{\frac{67}{1000000000000}\times \frac{4777600000000000000000000000000000000}{40589641}}{5.972}\times 10^{24}$$

Multiply \frac{67}{1000000000000} and \frac{4777600000000000000000000000000000000}{40589641} to get \frac{320099200000000000000000000}{40589641}.

$$\frac{\frac{320099200000000000000000000}{40589641}}{5.972}\times 10^{24}$$

Express \frac{\frac{320099200000000000000000000}{40589641}}{5.972} as a single fraction.

$$\frac{320099200000000000000000000}{40589641\times 5.972}\times 10^{24}$$

Multiply 40589641 and 5.972 to get 242401336.052.

$$\frac{320099200000000000000000000}{242401336.052}\times 10^{24}$$

Expand \frac{320099200000000000000000000}{242401336.052} by multiplying both numerator and the denominator by 1000.

$$\frac{320099200000000000000000000000}{242401336052}\times 10^{24}$$

Reduce the fraction \frac{320099200000000000000000000000}{242401336052} to lowest terms by extracting and canceling out 5972.

$$\frac{53600000000000000000000000}{40589641}\times 10^{24}$$

Calculate 10 to the power of 24 and get 1000000000000000000000000.

$$\frac{53600000000000000000000000}{40589641}\times 1000000000000000000000000$$

Multiply \frac{53600000000000000000000000}{40589641} and 1000000000000000000000000 to get \frac{53600000000000000000000000000000000000000000000000}{40589641}.

$$\frac{53600000000000000000000000000000000000000000000000}{40589641}$$

Factor

$$\frac{67 \cdot 2 ^ {50} \cdot 5 ^ {47}}{23 ^ {2} \cdot 277 ^ {2}} = 1.3205339756515708 \times 10^{42}\frac{22756938}{40589641} = 1.3205339756515708 \times 10^{42}$$