Solve 4*6*6710^-11/left(3*10right)^869551010^6left(1-frac{2*6*6710^-11{10}^30}{3{10}^83{10}^8695510{10}^6}right)

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

Evaluate

$$\frac{34949373011}{991806195130031250000000000000000000000000}\approx 3.523810719 \cdot 10^{-32}$$

Solution Steps

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

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

To multiply powers of the same base, add their exponents. Add 8 and 8 to get 16.

$$\frac{4\times 6\times 67\times 10^{-11}}{\left(3\times 10\right)^{8}\times 695510\times 10^{6}}\left(1-\frac{2\times 6\times 67\times 10^{19}}{3\times 10^{16}\times 3\times 695510\times 10^{6}}\right)$$

To multiply powers of the same base, add their exponents. Add 16 and 6 to get 22.

$$\frac{4\times 6\times 67\times 10^{-11}}{\left(3\times 10\right)^{8}\times 695510\times 10^{6}}\left(1-\frac{2\times 6\times 67\times 10^{19}}{3\times 10^{22}\times 3\times 695510}\right)$$

Cancel out 2 in both numerator and denominator.

$$\frac{2\times 6\times 67\times 10^{-11}}{347755\times 10^{6}\times \left(3\times 10\right)^{8}}\left(1-\frac{2\times 6\times 67\times 10^{19}}{3\times 10^{22}\times 3\times 695510}\right)$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{2\times 6\times 67}{347755\times 10^{17}\times \left(3\times 10\right)^{8}}\left(1-\frac{2\times 6\times 67\times 10^{19}}{3\times 10^{22}\times 3\times 695510}\right)$$

Multiply 2 and 6 to get 12.

$$\frac{12\times 67}{347755\times 10^{17}\times \left(3\times 10\right)^{8}}\left(1-\frac{2\times 6\times 67\times 10^{19}}{3\times 10^{22}\times 3\times 695510}\right)$$

Multiply 12 and 67 to get 804.

$$\frac{804}{347755\times 10^{17}\times \left(3\times 10\right)^{8}}\left(1-\frac{2\times 6\times 67\times 10^{19}}{3\times 10^{22}\times 3\times 695510}\right)$$

Calculate 10 to the power of 17 and get 100000000000000000.

$$\frac{804}{347755\times 100000000000000000\times \left(3\times 10\right)^{8}}\left(1-\frac{2\times 6\times 67\times 10^{19}}{3\times 10^{22}\times 3\times 695510}\right)$$

Multiply 347755 and 100000000000000000 to get 34775500000000000000000.

$$\frac{804}{34775500000000000000000\times \left(3\times 10\right)^{8}}\left(1-\frac{2\times 6\times 67\times 10^{19}}{3\times 10^{22}\times 3\times 695510}\right)$$

Multiply 3 and 10 to get 30.

$$\frac{804}{34775500000000000000000\times 30^{8}}\left(1-\frac{2\times 6\times 67\times 10^{19}}{3\times 10^{22}\times 3\times 695510}\right)$$

Calculate 30 to the power of 8 and get 656100000000.

$$\frac{804}{34775500000000000000000\times 656100000000}\left(1-\frac{2\times 6\times 67\times 10^{19}}{3\times 10^{22}\times 3\times 695510}\right)$$

Multiply 34775500000000000000000 and 656100000000 to get 22816205550000000000000000000000000.

$$\frac{804}{22816205550000000000000000000000000}\left(1-\frac{2\times 6\times 67\times 10^{19}}{3\times 10^{22}\times 3\times 695510}\right)$$

Reduce the fraction \frac{804}{22816205550000000000000000000000000} to lowest terms by extracting and canceling out 12.

$$\frac{67}{1901350462500000000000000000000000}\left(1-\frac{2\times 6\times 67\times 10^{19}}{3\times 10^{22}\times 3\times 695510}\right)$$

Cancel out 2\times 3\times 10^{19} in both numerator and denominator.

$$\frac{67}{1901350462500000000000000000000000}\left(1-\frac{2\times 67}{3\times 347755\times 10^{3}}\right)$$

Multiply 2 and 67 to get 134.

$$\frac{67}{1901350462500000000000000000000000}\left(1-\frac{134}{3\times 347755\times 10^{3}}\right)$$

Multiply 3 and 347755 to get 1043265.

$$\frac{67}{1901350462500000000000000000000000}\left(1-\frac{134}{1043265\times 10^{3}}\right)$$

Calculate 10 to the power of 3 and get 1000.

$$\frac{67}{1901350462500000000000000000000000}\left(1-\frac{134}{1043265\times 1000}\right)$$

Multiply 1043265 and 1000 to get 1043265000.

$$\frac{67}{1901350462500000000000000000000000}\left(1-\frac{134}{1043265000}\right)$$

Reduce the fraction \frac{134}{1043265000} to lowest terms by extracting and canceling out 2.

$$\frac{67}{1901350462500000000000000000000000}\left(1-\frac{67}{521632500}\right)$$

Subtract \frac{67}{521632500} from 1 to get \frac{521632433}{521632500}.

$$\frac{67}{1901350462500000000000000000000000}\times \frac{521632433}{521632500}$$

Multiply \frac{67}{1901350462500000000000000000000000} and \frac{521632433}{521632500} to get \frac{34949373011}{991806195130031250000000000000000000000000}.

$$\frac{34949373011}{991806195130031250000000000000000000000000}$$

Factor

$$\frac{7 \cdot 23 \cdot 67 \cdot 3239953}{2 ^ {25} \cdot 3 ^ {8} \cdot 5 ^ {30} \cdot 157 ^ {2} \cdot 443 ^ {2}} = 3.5238107185263083 \times 10^{-32}$$