Solve frac{4*6,67*10^{-11}*2*10^{30}}{(3*10^{9})^{2}*(695510*10^{6})^{2}}(1-frac{2*6,67*10^{-11}*2*10^30}{(3*10^8)^2695510*10^6})

$$\frac { 4 \times 6,67 \times 10 ^ { - 11 } \times 2 \times 10 ^ { 30 } } { ( 3 \times 10 ^ { 9 } ) ^ { 2 } \times ( 695510 \times 10 ^ { 6 } ) ^ { 2 } } ( 1 - \frac { 2 \times 6,67 \times 10 ^ { - 11 } \times 2 \times 10 ^ { 30 } } { ( 3 \times 10 ^ { 8 } ) ^ { 2 } 695510 \times 10 ^ { 6 } } )$$

Evaluate

$$\frac{104378662805111}{851618675030725968750000000000000000}\approx 1,225650234 \cdot 10^{-22}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -11 and 30 to get 19.

$$\frac{4\times 6,67\times 10^{19}\times 2}{\left(3\times 10^{9}\right)^{2}\times \left(695510\times 10^{6}\right)^{2}}\left(1-\frac{2\times 6,67\times 10^{-11}\times 2\times 10^{30}}{\left(3\times 10^{8}\right)^{2}\times 695510\times 10^{6}}\right)$$

To multiply powers of the same base, add their exponents. Add -11 and 30 to get 19.

$$\frac{4\times 6,67\times 10^{19}\times 2}{\left(3\times 10^{9}\right)^{2}\times \left(695510\times 10^{6}\right)^{2}}\left(1-\frac{2\times 6,67\times 10^{19}\times 2}{\left(3\times 10^{8}\right)^{2}\times 695510\times 10^{6}}\right)$$

Multiply 4 and 6,67 to get 26,68.

$$\frac{26,68\times 10^{19}\times 2}{\left(3\times 10^{9}\right)^{2}\times \left(695510\times 10^{6}\right)^{2}}\left(1-\frac{2\times 6,67\times 10^{19}\times 2}{\left(3\times 10^{8}\right)^{2}\times 695510\times 10^{6}}\right)$$

Calculate 10 to the power of 19 and get 10000000000000000000.

$$\frac{26,68\times 10000000000000000000\times 2}{\left(3\times 10^{9}\right)^{2}\times \left(695510\times 10^{6}\right)^{2}}\left(1-\frac{2\times 6,67\times 10^{19}\times 2}{\left(3\times 10^{8}\right)^{2}\times 695510\times 10^{6}}\right)$$

Multiply 26,68 and 10000000000000000000 to get 266800000000000000000.

$$\frac{266800000000000000000\times 2}{\left(3\times 10^{9}\right)^{2}\times \left(695510\times 10^{6}\right)^{2}}\left(1-\frac{2\times 6,67\times 10^{19}\times 2}{\left(3\times 10^{8}\right)^{2}\times 695510\times 10^{6}}\right)$$

Multiply 266800000000000000000 and 2 to get 533600000000000000000.

$$\frac{533600000000000000000}{\left(3\times 10^{9}\right)^{2}\times \left(695510\times 10^{6}\right)^{2}}\left(1-\frac{2\times 6,67\times 10^{19}\times 2}{\left(3\times 10^{8}\right)^{2}\times 695510\times 10^{6}}\right)$$

Calculate 10 to the power of 9 and get 1000000000.

$$\frac{533600000000000000000}{\left(3\times 1000000000\right)^{2}\times \left(695510\times 10^{6}\right)^{2}}\left(1-\frac{2\times 6,67\times 10^{19}\times 2}{\left(3\times 10^{8}\right)^{2}\times 695510\times 10^{6}}\right)$$

Multiply 3 and 1000000000 to get 3000000000.

$$\frac{533600000000000000000}{3000000000^{2}\times \left(695510\times 10^{6}\right)^{2}}\left(1-\frac{2\times 6,67\times 10^{19}\times 2}{\left(3\times 10^{8}\right)^{2}\times 695510\times 10^{6}}\right)$$

Calculate 3000000000 to the power of 2 and get 9000000000000000000.

$$\frac{533600000000000000000}{9000000000000000000\times \left(695510\times 10^{6}\right)^{2}}\left(1-\frac{2\times 6,67\times 10^{19}\times 2}{\left(3\times 10^{8}\right)^{2}\times 695510\times 10^{6}}\right)$$

Calculate 10 to the power of 6 and get 1000000.

$$\frac{533600000000000000000}{9000000000000000000\times \left(695510\times 1000000\right)^{2}}\left(1-\frac{2\times 6,67\times 10^{19}\times 2}{\left(3\times 10^{8}\right)^{2}\times 695510\times 10^{6}}\right)$$

Multiply 695510 and 1000000 to get 695510000000.

$$\frac{533600000000000000000}{9000000000000000000\times 695510000000^{2}}\left(1-\frac{2\times 6,67\times 10^{19}\times 2}{\left(3\times 10^{8}\right)^{2}\times 695510\times 10^{6}}\right)$$

Calculate 695510000000 to the power of 2 and get 483734160100000000000000.

$$\frac{533600000000000000000}{9000000000000000000\times 483734160100000000000000}\left(1-\frac{2\times 6,67\times 10^{19}\times 2}{\left(3\times 10^{8}\right)^{2}\times 695510\times 10^{6}}\right)$$

Multiply 9000000000000000000 and 483734160100000000000000 to get 4353607440900000000000000000000000000000000.

$$\frac{533600000000000000000}{4353607440900000000000000000000000000000000}\left(1-\frac{2\times 6,67\times 10^{19}\times 2}{\left(3\times 10^{8}\right)^{2}\times 695510\times 10^{6}}\right)$$

Reduce the fraction \frac{533600000000000000000}{4353607440900000000000000000000000000000000} to lowest terms by extracting and canceling out 800000000000000000.

$$\frac{667}{5442009301125000000000000}\left(1-\frac{2\times 6,67\times 10^{19}\times 2}{\left(3\times 10^{8}\right)^{2}\times 695510\times 10^{6}}\right)$$

Cancel out 2\times 10^{6} in both numerator and denominator.

$$\frac{667}{5442009301125000000000000}\left(1-\frac{2\times 6,67\times 10^{13}}{347755\times \left(3\times 10^{8}\right)^{2}}\right)$$

Multiply 2 and 6,67 to get 13,34.

$$\frac{667}{5442009301125000000000000}\left(1-\frac{13,34\times 10^{13}}{347755\times \left(3\times 10^{8}\right)^{2}}\right)$$

Calculate 10 to the power of 13 and get 10000000000000.

$$\frac{667}{5442009301125000000000000}\left(1-\frac{13,34\times 10000000000000}{347755\times \left(3\times 10^{8}\right)^{2}}\right)$$

Multiply 13,34 and 10000000000000 to get 133400000000000.

$$\frac{667}{5442009301125000000000000}\left(1-\frac{133400000000000}{347755\times \left(3\times 10^{8}\right)^{2}}\right)$$

Calculate 10 to the power of 8 and get 100000000.

$$\frac{667}{5442009301125000000000000}\left(1-\frac{133400000000000}{347755\times \left(3\times 100000000\right)^{2}}\right)$$

Multiply 3 and 100000000 to get 300000000.

$$\frac{667}{5442009301125000000000000}\left(1-\frac{133400000000000}{347755\times 300000000^{2}}\right)$$

Calculate 300000000 to the power of 2 and get 90000000000000000.

$$\frac{667}{5442009301125000000000000}\left(1-\frac{133400000000000}{347755\times 90000000000000000}\right)$$

Multiply 347755 and 90000000000000000 to get 31297950000000000000000.

$$\frac{667}{5442009301125000000000000}\left(1-\frac{133400000000000}{31297950000000000000000}\right)$$

Reduce the fraction \frac{133400000000000}{31297950000000000000000} to lowest terms by extracting and canceling out 200000000000.

$$\frac{667}{5442009301125000000000000}\left(1-\frac{667}{156489750000}\right)$$

Subtract \frac{667}{156489750000} from 1 to get \frac{156489749333}{156489750000}.

$$\frac{667}{5442009301125000000000000}\times \frac{156489749333}{156489750000}$$

Multiply \frac{667}{5442009301125000000000000} and \frac{156489749333}{156489750000} to get \frac{104378662805111}{851618675030725968750000000000000000}.

$$\frac{104378662805111}{851618675030725968750000000000000000}$$

Factor

$$\frac{23 \cdot 29 \cdot 156489749333}{2 ^ {16} \cdot 3 ^ {4} \cdot 5 ^ {21} \cdot 157 ^ {3} \cdot 443 ^ {3}} = 1.2256502336723072 \times 10^{-22}$$