Solve 2*6.67*10^-11*(7.33*10^22/1.7*10^6-7.33*10^22/4.7*{10^{6}}-frac{6*{10}^24}{3.834*{10}^8}+frac{6*{10}^24}{3.864*{10}^8})

$$2 \times 6.67 \times { 10 }^{ -11 } \times ( \frac{ 7.33 \times { 10 }^{ 22 } }{ 1.7 \times { 10 }^{ 6 } } - \frac{ 7.33 \times { 10 }^{ 22 } }{ 4.7 \times { 10 }^{ 6 } } - \frac{ 6 \times { 10 }^{ 24 } }{ 3.834 \times { 10 }^{ 8 } } + \frac{ 6 \times { 10 }^{ 24 } }{ 3.864 \times { 10 }^{ 8 } } )$$

Evaluate

$$\frac{13063465918000}{3573927}\approx 3655213.415942743$$

Solution Steps

Multiply 2 and 6.67 to get 13.34.

$$13.34\times 10^{-11}\left(\frac{7.33\times 10^{22}}{1.7\times 10^{6}}-\frac{7.33\times 10^{22}}{4.7\times 10^{6}}-\frac{6\times 10^{24}}{3.834\times 10^{8}}+\frac{6\times 10^{24}}{3.864\times 10^{8}}\right)$$

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

$$13.34\times \frac{1}{100000000000}\left(\frac{7.33\times 10^{22}}{1.7\times 10^{6}}-\frac{7.33\times 10^{22}}{4.7\times 10^{6}}-\frac{6\times 10^{24}}{3.834\times 10^{8}}+\frac{6\times 10^{24}}{3.864\times 10^{8}}\right)$$

Multiply 13.34 and \frac{1}{100000000000} to get \frac{667}{5000000000000}.

$$\frac{667}{5000000000000}\left(\frac{7.33\times 10^{22}}{1.7\times 10^{6}}-\frac{7.33\times 10^{22}}{4.7\times 10^{6}}-\frac{6\times 10^{24}}{3.834\times 10^{8}}+\frac{6\times 10^{24}}{3.864\times 10^{8}}\right)$$

Cancel out 10^{6} in both numerator and denominator.

$$\frac{667}{5000000000000}\left(\frac{7.33\times 10^{16}}{1.7}-\frac{7.33\times 10^{22}}{4.7\times 10^{6}}-\frac{6\times 10^{24}}{3.834\times 10^{8}}+\frac{6\times 10^{24}}{3.864\times 10^{8}}\right)$$

Calculate 10 to the power of 16 and get 10000000000000000.

$$\frac{667}{5000000000000}\left(\frac{7.33\times 10000000000000000}{1.7}-\frac{7.33\times 10^{22}}{4.7\times 10^{6}}-\frac{6\times 10^{24}}{3.834\times 10^{8}}+\frac{6\times 10^{24}}{3.864\times 10^{8}}\right)$$

Multiply 7.33 and 10000000000000000 to get 73300000000000000.

$$\frac{667}{5000000000000}\left(\frac{73300000000000000}{1.7}-\frac{7.33\times 10^{22}}{4.7\times 10^{6}}-\frac{6\times 10^{24}}{3.834\times 10^{8}}+\frac{6\times 10^{24}}{3.864\times 10^{8}}\right)$$

Expand \frac{73300000000000000}{1.7} by multiplying both numerator and the denominator by 10.

$$\frac{667}{5000000000000}\left(\frac{733000000000000000}{17}-\frac{7.33\times 10^{22}}{4.7\times 10^{6}}-\frac{6\times 10^{24}}{3.834\times 10^{8}}+\frac{6\times 10^{24}}{3.864\times 10^{8}}\right)$$

Cancel out 10^{6} in both numerator and denominator.

$$\frac{667}{5000000000000}\left(\frac{733000000000000000}{17}-\frac{7.33\times 10^{16}}{4.7}-\frac{6\times 10^{24}}{3.834\times 10^{8}}+\frac{6\times 10^{24}}{3.864\times 10^{8}}\right)$$

Calculate 10 to the power of 16 and get 10000000000000000.

$$\frac{667}{5000000000000}\left(\frac{733000000000000000}{17}-\frac{7.33\times 10000000000000000}{4.7}-\frac{6\times 10^{24}}{3.834\times 10^{8}}+\frac{6\times 10^{24}}{3.864\times 10^{8}}\right)$$

Multiply 7.33 and 10000000000000000 to get 73300000000000000.

$$\frac{667}{5000000000000}\left(\frac{733000000000000000}{17}-\frac{73300000000000000}{4.7}-\frac{6\times 10^{24}}{3.834\times 10^{8}}+\frac{6\times 10^{24}}{3.864\times 10^{8}}\right)$$

Expand \frac{73300000000000000}{4.7} by multiplying both numerator and the denominator by 10.

$$\frac{667}{5000000000000}\left(\frac{733000000000000000}{17}-\frac{733000000000000000}{47}-\frac{6\times 10^{24}}{3.834\times 10^{8}}+\frac{6\times 10^{24}}{3.864\times 10^{8}}\right)$$

Subtract \frac{733000000000000000}{47} from \frac{733000000000000000}{17} to get \frac{21990000000000000000}{799}.

$$\frac{667}{5000000000000}\left(\frac{21990000000000000000}{799}-\frac{6\times 10^{24}}{3.834\times 10^{8}}+\frac{6\times 10^{24}}{3.864\times 10^{8}}\right)$$

Cancel out 10^{8} in both numerator and denominator.

$$\frac{667}{5000000000000}\left(\frac{21990000000000000000}{799}-\frac{6\times 10^{16}}{3.834}+\frac{6\times 10^{24}}{3.864\times 10^{8}}\right)$$

Calculate 10 to the power of 16 and get 10000000000000000.

$$\frac{667}{5000000000000}\left(\frac{21990000000000000000}{799}-\frac{6\times 10000000000000000}{3.834}+\frac{6\times 10^{24}}{3.864\times 10^{8}}\right)$$

Multiply 6 and 10000000000000000 to get 60000000000000000.

$$\frac{667}{5000000000000}\left(\frac{21990000000000000000}{799}-\frac{60000000000000000}{3.834}+\frac{6\times 10^{24}}{3.864\times 10^{8}}\right)$$

Expand \frac{60000000000000000}{3.834} by multiplying both numerator and the denominator by 1000.

$$\frac{667}{5000000000000}\left(\frac{21990000000000000000}{799}-\frac{60000000000000000000}{3834}+\frac{6\times 10^{24}}{3.864\times 10^{8}}\right)$$

Reduce the fraction \frac{60000000000000000000}{3834} to lowest terms by extracting and canceling out 6.

$$\frac{667}{5000000000000}\left(\frac{21990000000000000000}{799}-\frac{10000000000000000000}{639}+\frac{6\times 10^{24}}{3.864\times 10^{8}}\right)$$

Subtract \frac{10000000000000000000}{639} from \frac{21990000000000000000}{799} to get \frac{6061610000000000000000}{510561}.

$$\frac{667}{5000000000000}\left(\frac{6061610000000000000000}{510561}+\frac{6\times 10^{24}}{3.864\times 10^{8}}\right)$$

Cancel out 10^{8} in both numerator and denominator.

$$\frac{667}{5000000000000}\left(\frac{6061610000000000000000}{510561}+\frac{6\times 10^{16}}{3.864}\right)$$

Calculate 10 to the power of 16 and get 10000000000000000.

$$\frac{667}{5000000000000}\left(\frac{6061610000000000000000}{510561}+\frac{6\times 10000000000000000}{3.864}\right)$$

Multiply 6 and 10000000000000000 to get 60000000000000000.

$$\frac{667}{5000000000000}\left(\frac{6061610000000000000000}{510561}+\frac{60000000000000000}{3.864}\right)$$

Expand \frac{60000000000000000}{3.864} by multiplying both numerator and the denominator by 1000.

$$\frac{667}{5000000000000}\left(\frac{6061610000000000000000}{510561}+\frac{60000000000000000000}{3864}\right)$$

Reduce the fraction \frac{60000000000000000000}{3864} to lowest terms by extracting and canceling out 24.

$$\frac{667}{5000000000000}\left(\frac{6061610000000000000000}{510561}+\frac{2500000000000000000}{161}\right)$$

Add \frac{6061610000000000000000}{510561} and \frac{2500000000000000000}{161} to get \frac{2252321710000000000000000}{82200321}.

$$\frac{667}{5000000000000}\times \frac{2252321710000000000000000}{82200321}$$

Multiply \frac{667}{5000000000000} and \frac{2252321710000000000000000}{82200321} to get \frac{13063465918000}{3573927}.

$$\frac{13063465918000}{3573927}$$

Factor

$$\frac{29 \cdot 225232171 \cdot 2 ^ {4} \cdot 5 ^ {3}}{7 \cdot 17 \cdot 47 \cdot 71 \cdot 3 ^ {2}} = 3655213\frac{1486549}{3573927} = 3655213.415942743$$