Resolver 316*9*10^9left(1.6*10^-19right)^2/6.64*10^-27{left(5*{10^7right)}^-2}

$$\frac{ 316 \cdot 9 \times { 10 }^{ 9 } { \left(1.6 \times { 10 }^{ -19 } \right) }^{ 2 } }{ 6.64 \times { 10 }^{ -27 } { \left(5 \times { 10 }^{ 7 } \right) }^{ -2 } }$$

Calcular

$$\frac{2275200000000000000}{83}\approx 2.741204819 \cdot 10^{16}$$

Pasos da solución

Para dividir potencias da mesma base, resta o expoñente do denominador do expoñente do numerador.

$$\frac{9\times 316\times 10^{36}\times \left(1.6\times 10^{-19}\right)^{2}}{6.64\times \left(5\times 10^{7}\right)^{-2}}$$

Multiplica 9 e 316 para obter 2844.

$$\frac{2844\times 10^{36}\times \left(1.6\times 10^{-19}\right)^{2}}{6.64\times \left(5\times 10^{7}\right)^{-2}}$$

Calcula 10 á potencia de 36 e obtén 1000000000000000000000000000000000000.

$$\frac{2844\times 1000000000000000000000000000000000000\times \left(1.6\times 10^{-19}\right)^{2}}{6.64\times \left(5\times 10^{7}\right)^{-2}}$$

Multiplica 2844 e 1000000000000000000000000000000000000 para obter 2844000000000000000000000000000000000000.

$$\frac{2844000000000000000000000000000000000000\times \left(1.6\times 10^{-19}\right)^{2}}{6.64\times \left(5\times 10^{7}\right)^{-2}}$$

Calcula 10 á potencia de -19 e obtén \frac{1}{10000000000000000000}.

$$\frac{2844000000000000000000000000000000000000\times \left(1.6\times \frac{1}{10000000000000000000}\right)^{2}}{6.64\times \left(5\times 10^{7}\right)^{-2}}$$

Multiplica 1.6 e \frac{1}{10000000000000000000} para obter \frac{1}{6250000000000000000}.

$$\frac{2844000000000000000000000000000000000000\times \left(\frac{1}{6250000000000000000}\right)^{2}}{6.64\times \left(5\times 10^{7}\right)^{-2}}$$

Calcula \frac{1}{6250000000000000000} á potencia de 2 e obtén \frac{1}{39062500000000000000000000000000000000}.

$$\frac{2844000000000000000000000000000000000000\times \frac{1}{39062500000000000000000000000000000000}}{6.64\times \left(5\times 10^{7}\right)^{-2}}$$

Multiplica 2844000000000000000000000000000000000000 e \frac{1}{39062500000000000000000000000000000000} para obter \frac{45504}{625}.

$$\frac{\frac{45504}{625}}{6.64\times \left(5\times 10^{7}\right)^{-2}}$$

Calcula 10 á potencia de 7 e obtén 10000000.

$$\frac{\frac{45504}{625}}{6.64\times \left(5\times 10000000\right)^{-2}}$$

Multiplica 5 e 10000000 para obter 50000000.

$$\frac{\frac{45504}{625}}{6.64\times 50000000^{-2}}$$

Calcula 50000000 á potencia de -2 e obtén \frac{1}{2500000000000000}.

$$\frac{\frac{45504}{625}}{6.64\times \frac{1}{2500000000000000}}$$

Multiplica 6.64 e \frac{1}{2500000000000000} para obter \frac{83}{31250000000000000}.

$$\frac{\frac{45504}{625}}{\frac{83}{31250000000000000}}$$

Divide \frac{45504}{625} entre \frac{83}{31250000000000000} mediante a multiplicación de \frac{45504}{625} polo recíproco de \frac{83}{31250000000000000}.

$$\frac{45504}{625}\times \frac{31250000000000000}{83}$$

Multiplica \frac{45504}{625} e \frac{31250000000000000}{83} para obter \frac{2275200000000000000}{83}.

$$\frac{2275200000000000000}{83}$$

Factorizar

$$\frac{79 \cdot 2 ^ {19} \cdot 3 ^ {2} \cdot 5 ^ {14}}{83} = 27412048192771084\frac{28}{83} = 27412048192771084$$