Resolver 6.67*10^-14*7.4*10^12/(1740*10^11)^2

$$\frac { 6.67 \times 10 ^ { - 14 } \times 7.4 \times 10 ^ { 12 } } { ( 1740 \times 10 ^ { 11 } ) ^ { 2 } }$$

Calcular

$$\frac{851}{52200000000000000000000000000000}\approx 1.630268199 \cdot 10^{-29}$$

Pasos da solución

Para multiplicar potencias da mesma base, suma os seus expoñentes. Suma -14 e 12 para obter -2.

$$\frac{6.67\times 10^{-2}\times 7.4}{\left(1740\times 10^{11}\right)^{2}}$$

Calcula 10 á potencia de -2 e obtén \frac{1}{100}.

$$\frac{6.67\times \frac{1}{100}\times 7.4}{\left(1740\times 10^{11}\right)^{2}}$$

Multiplica 6.67 e \frac{1}{100} para obter \frac{667}{10000}.

$$\frac{\frac{667}{10000}\times 7.4}{\left(1740\times 10^{11}\right)^{2}}$$

Multiplica \frac{667}{10000} e 7.4 para obter \frac{24679}{50000}.

$$\frac{\frac{24679}{50000}}{\left(1740\times 10^{11}\right)^{2}}$$

Calcula 10 á potencia de 11 e obtén 100000000000.

$$\frac{\frac{24679}{50000}}{\left(1740\times 100000000000\right)^{2}}$$

Multiplica 1740 e 100000000000 para obter 174000000000000.

$$\frac{\frac{24679}{50000}}{174000000000000^{2}}$$

Calcula 174000000000000 á potencia de 2 e obtén 30276000000000000000000000000.

$$\frac{\frac{24679}{50000}}{30276000000000000000000000000}$$

Expresa \frac{\frac{24679}{50000}}{30276000000000000000000000000} como unha única fracción.

$$\frac{24679}{50000\times 30276000000000000000000000000}$$

Multiplica 50000 e 30276000000000000000000000000 para obter 1513800000000000000000000000000000.

$$\frac{24679}{1513800000000000000000000000000000}$$

Reduce a fracción \frac{24679}{1513800000000000000000000000000000} a termos máis baixos extraendo e cancelando 29.

$$\frac{851}{52200000000000000000000000000000}$$

Factorizar

$$\frac{23 \cdot 37}{29 \cdot 2 ^ {30} \cdot 3 ^ {2} \cdot 5 ^ {29}} = 1.6302681992337167 \times 10^{-29}$$