Resolver frac{9*10^{9}*(16*10^{-19})^2}{667*10^11*91*10^-31*166*10^-27}

$$\frac { 9 \times 10 ^ { 9 } \times ( 16 \times 10 ^ { - 19 } ) ^ { 2 } } { 667 \times 10 ^ { 11 } \times 91 \times 10 ^ { - 31 } \times 166 \times 10 ^ { - 27 } }$$

Calcular

$$\frac{1152000000000000000000}{5037851}\approx 2.286689305 \cdot 10^{14}$$

Pasos da solución

Para multiplicar potencias da mesma base, suma os seus expoñentes. Suma 11 e -31 para obter -20.

$$\frac{9\times 10^{9}\times \left(16\times 10^{-19}\right)^{2}}{667\times 10^{-20}\times 91\times 166\times 10^{-27}}$$

Para multiplicar potencias da mesma base, suma os seus expoñentes. Suma -20 e -27 para obter -47.

$$\frac{9\times 10^{9}\times \left(16\times 10^{-19}\right)^{2}}{667\times 10^{-47}\times 91\times 166}$$

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

$$\frac{9\times 10^{56}\times \left(16\times 10^{-19}\right)^{2}}{91\times 166\times 667}$$

Calcula 10 á potencia de 56 e obtén 100000000000000000000000000000000000000000000000000000000.

$$\frac{9\times 100000000000000000000000000000000000000000000000000000000\times \left(16\times 10^{-19}\right)^{2}}{91\times 166\times 667}$$

Multiplica 9 e 100000000000000000000000000000000000000000000000000000000 para obter 900000000000000000000000000000000000000000000000000000000.

$$\frac{900000000000000000000000000000000000000000000000000000000\times \left(16\times 10^{-19}\right)^{2}}{91\times 166\times 667}$$

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

$$\frac{900000000000000000000000000000000000000000000000000000000\times \left(16\times \frac{1}{10000000000000000000}\right)^{2}}{91\times 166\times 667}$$

Multiplica 16 e \frac{1}{10000000000000000000} para obter \frac{1}{625000000000000000}.

$$\frac{900000000000000000000000000000000000000000000000000000000\times \left(\frac{1}{625000000000000000}\right)^{2}}{91\times 166\times 667}$$

Calcula \frac{1}{625000000000000000} á potencia de 2 e obtén \frac{1}{390625000000000000000000000000000000}.

$$\frac{900000000000000000000000000000000000000000000000000000000\times \frac{1}{390625000000000000000000000000000000}}{91\times 166\times 667}$$

Multiplica 900000000000000000000000000000000000000000000000000000000 e \frac{1}{390625000000000000000000000000000000} para obter 2304000000000000000000.

$$\frac{2304000000000000000000}{91\times 166\times 667}$$

Multiplica 91 e 166 para obter 15106.

$$\frac{2304000000000000000000}{15106\times 667}$$

Multiplica 15106 e 667 para obter 10075702.

$$\frac{2304000000000000000000}{10075702}$$

Reduce a fracción \frac{2304000000000000000000}{10075702} a termos máis baixos extraendo e cancelando 2.

$$\frac{1152000000000000000000}{5037851}$$

Factorizar

$$\frac{2 ^ {25} \cdot 3 ^ {2} \cdot 5 ^ {18}}{7 \cdot 13 \cdot 23 \cdot 29 \cdot 83} = 228668930462611\frac{4711039}{5037851} = 228668930462611.94$$