Resolver 4*6*6710^-11210^30/left(310^3right)^2{left(695510{10^{6}right)}^{2}}left(1-frac{2*6*67{10}^{-11}2{10}^30}{{left(3{10}^8right)}^2*695510{10}^6}right)

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

Avaliar

$$\frac{69898737044}{9462429722563621875}\approx 7,386975554 \cdot 10^{-9}$$

Passos Para a Resolução

Para multiplicar as potências da mesma base, some os seus expoentes. Some -11 e 30 para obter 19.

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

Para multiplicar as potências da mesma base, some os seus expoentes. Some -11 e 30 para obter 19.

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

Multiplique 4 e 6 para obter 24.

$$\frac{24\times 67\times 10^{19}\times 2}{\left(3\times 10^{3}\right)^{2}\times \left(695510\times 10^{6}\right)^{2}}\left(1-\frac{2\times 6\times 67\times 10^{19}\times 2}{\left(3\times 10^{8}\right)^{2}\times 695510\times 10^{6}}\right)$$

Multiplique 24 e 67 para obter 1608.

$$\frac{1608\times 10^{19}\times 2}{\left(3\times 10^{3}\right)^{2}\times \left(695510\times 10^{6}\right)^{2}}\left(1-\frac{2\times 6\times 67\times 10^{19}\times 2}{\left(3\times 10^{8}\right)^{2}\times 695510\times 10^{6}}\right)$$

Calcule 10 elevado a 19 e obtenha 10000000000000000000.

$$\frac{1608\times 10000000000000000000\times 2}{\left(3\times 10^{3}\right)^{2}\times \left(695510\times 10^{6}\right)^{2}}\left(1-\frac{2\times 6\times 67\times 10^{19}\times 2}{\left(3\times 10^{8}\right)^{2}\times 695510\times 10^{6}}\right)$$

Multiplique 1608 e 10000000000000000000 para obter 16080000000000000000000.

$$\frac{16080000000000000000000\times 2}{\left(3\times 10^{3}\right)^{2}\times \left(695510\times 10^{6}\right)^{2}}\left(1-\frac{2\times 6\times 67\times 10^{19}\times 2}{\left(3\times 10^{8}\right)^{2}\times 695510\times 10^{6}}\right)$$

Multiplique 16080000000000000000000 e 2 para obter 32160000000000000000000.

$$\frac{32160000000000000000000}{\left(3\times 10^{3}\right)^{2}\times \left(695510\times 10^{6}\right)^{2}}\left(1-\frac{2\times 6\times 67\times 10^{19}\times 2}{\left(3\times 10^{8}\right)^{2}\times 695510\times 10^{6}}\right)$$

Calcule 10 elevado a 3 e obtenha 1000.

$$\frac{32160000000000000000000}{\left(3\times 1000\right)^{2}\times \left(695510\times 10^{6}\right)^{2}}\left(1-\frac{2\times 6\times 67\times 10^{19}\times 2}{\left(3\times 10^{8}\right)^{2}\times 695510\times 10^{6}}\right)$$

Multiplique 3 e 1000 para obter 3000.

$$\frac{32160000000000000000000}{3000^{2}\times \left(695510\times 10^{6}\right)^{2}}\left(1-\frac{2\times 6\times 67\times 10^{19}\times 2}{\left(3\times 10^{8}\right)^{2}\times 695510\times 10^{6}}\right)$$

Calcule 3000 elevado a 2 e obtenha 9000000.

$$\frac{32160000000000000000000}{9000000\times \left(695510\times 10^{6}\right)^{2}}\left(1-\frac{2\times 6\times 67\times 10^{19}\times 2}{\left(3\times 10^{8}\right)^{2}\times 695510\times 10^{6}}\right)$$

Calcule 10 elevado a 6 e obtenha 1000000.

$$\frac{32160000000000000000000}{9000000\times \left(695510\times 1000000\right)^{2}}\left(1-\frac{2\times 6\times 67\times 10^{19}\times 2}{\left(3\times 10^{8}\right)^{2}\times 695510\times 10^{6}}\right)$$

Multiplique 695510 e 1000000 para obter 695510000000.

$$\frac{32160000000000000000000}{9000000\times 695510000000^{2}}\left(1-\frac{2\times 6\times 67\times 10^{19}\times 2}{\left(3\times 10^{8}\right)^{2}\times 695510\times 10^{6}}\right)$$

Calcule 695510000000 elevado a 2 e obtenha 483734160100000000000000.

$$\frac{32160000000000000000000}{9000000\times 483734160100000000000000}\left(1-\frac{2\times 6\times 67\times 10^{19}\times 2}{\left(3\times 10^{8}\right)^{2}\times 695510\times 10^{6}}\right)$$

Multiplique 9000000 e 483734160100000000000000 para obter 4353607440900000000000000000000.

$$\frac{32160000000000000000000}{4353607440900000000000000000000}\left(1-\frac{2\times 6\times 67\times 10^{19}\times 2}{\left(3\times 10^{8}\right)^{2}\times 695510\times 10^{6}}\right)$$

Reduza a fração \frac{32160000000000000000000}{4353607440900000000000000000000} para os termos mais baixos ao retirar e anular 60000000000000000000.

$$\frac{536}{72560124015}\left(1-\frac{2\times 6\times 67\times 10^{19}\times 2}{\left(3\times 10^{8}\right)^{2}\times 695510\times 10^{6}}\right)$$

Anule 2\times 10^{6} no numerador e no denominador.

$$\frac{536}{72560124015}\left(1-\frac{2\times 6\times 67\times 10^{13}}{347755\times \left(3\times 10^{8}\right)^{2}}\right)$$

Multiplique 2 e 6 para obter 12.

$$\frac{536}{72560124015}\left(1-\frac{12\times 67\times 10^{13}}{347755\times \left(3\times 10^{8}\right)^{2}}\right)$$

Multiplique 12 e 67 para obter 804.

$$\frac{536}{72560124015}\left(1-\frac{804\times 10^{13}}{347755\times \left(3\times 10^{8}\right)^{2}}\right)$$

Calcule 10 elevado a 13 e obtenha 10000000000000.

$$\frac{536}{72560124015}\left(1-\frac{804\times 10000000000000}{347755\times \left(3\times 10^{8}\right)^{2}}\right)$$

Multiplique 804 e 10000000000000 para obter 8040000000000000.

$$\frac{536}{72560124015}\left(1-\frac{8040000000000000}{347755\times \left(3\times 10^{8}\right)^{2}}\right)$$

Calcule 10 elevado a 8 e obtenha 100000000.

$$\frac{536}{72560124015}\left(1-\frac{8040000000000000}{347755\times \left(3\times 100000000\right)^{2}}\right)$$

Multiplique 3 e 100000000 para obter 300000000.

$$\frac{536}{72560124015}\left(1-\frac{8040000000000000}{347755\times 300000000^{2}}\right)$$

Calcule 300000000 elevado a 2 e obtenha 90000000000000000.

$$\frac{536}{72560124015}\left(1-\frac{8040000000000000}{347755\times 90000000000000000}\right)$$

Multiplique 347755 e 90000000000000000 para obter 31297950000000000000000.

$$\frac{536}{72560124015}\left(1-\frac{8040000000000000}{31297950000000000000000}\right)$$

Reduza a fração \frac{8040000000000000}{31297950000000000000000} para os termos mais baixos ao retirar e anular 120000000000000.

$$\frac{536}{72560124015}\left(1-\frac{67}{260816250}\right)$$

Subtraia \frac{67}{260816250} de 1 para obter \frac{260816183}{260816250}.

$$\frac{536}{72560124015}\times \frac{260816183}{260816250}$$

Multiplique \frac{536}{72560124015} e \frac{260816183}{260816250} para obter \frac{69898737044}{9462429722563621875}.

$$\frac{69898737044}{9462429722563621875}$$

Fatorizar

$$\frac{2 ^ {2} \cdot 67 \cdot 260816183}{3 ^ {2} \cdot 5 ^ {5} \cdot 157 ^ {3} \cdot 443 ^ {3}} = 7,386975554209198 \times 10^{-9}$$