Solucionar frac{3^{2}*(6*626*10^-34)^2}{8*9*1*10^-31*(4805*10^-9)}

$$\frac { 3 ^ { 2 } \times ( 6 \cdot 626 \times 10 ^ { - 34 } ) ^ { 2 } } { 8 \times 9 \cdot 1 \times 10 ^ { - 31 } \times ( 4805 \times 10 ^ { - 9 } ) }$$

Calcular

$$\frac{881721}{24025000000000000000000000000000}\approx 3,670014568 \cdot 10^{-26}$$

Pasos de la solución

Para multiplicar potencias de la misma base, sume sus exponentes. Sume -31 y -9 para obtener -40.

$$\frac{3^{2}\times \left(6\times 626\times 10^{-34}\right)^{2}}{8\times 9\times 1\times 10^{-40}\times 4805}$$

Calcula 3 a la potencia de 2 y obtiene 9.

$$\frac{9\times \left(6\times 626\times 10^{-34}\right)^{2}}{8\times 9\times 1\times 10^{-40}\times 4805}$$

Multiplica 6 y 626 para obtener 3756.

$$\frac{9\times \left(3756\times 10^{-34}\right)^{2}}{8\times 9\times 1\times 10^{-40}\times 4805}$$

Calcula 10 a la potencia de -34 y obtiene \frac{1}{10000000000000000000000000000000000}.

$$\frac{9\times \left(3756\times \frac{1}{10000000000000000000000000000000000}\right)^{2}}{8\times 9\times 1\times 10^{-40}\times 4805}$$

Multiplica 3756 y \frac{1}{10000000000000000000000000000000000} para obtener \frac{939}{2500000000000000000000000000000000}.

$$\frac{9\times \left(\frac{939}{2500000000000000000000000000000000}\right)^{2}}{8\times 9\times 1\times 10^{-40}\times 4805}$$

Calcula \frac{939}{2500000000000000000000000000000000} a la potencia de 2 y obtiene \frac{881721}{6250000000000000000000000000000000000000000000000000000000000000000}.

$$\frac{9\times \frac{881721}{6250000000000000000000000000000000000000000000000000000000000000000}}{8\times 9\times 1\times 10^{-40}\times 4805}$$

Multiplica 9 y \frac{881721}{6250000000000000000000000000000000000000000000000000000000000000000} para obtener \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000}.

$$\frac{\frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000}}{8\times 9\times 1\times 10^{-40}\times 4805}$$

Multiplica 8 y 9 para obtener 72.

$$\frac{\frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000}}{72\times 1\times 10^{-40}\times 4805}$$

Multiplica 72 y 1 para obtener 72.

$$\frac{\frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000}}{72\times 10^{-40}\times 4805}$$

Calcula 10 a la potencia de -40 y obtiene \frac{1}{10000000000000000000000000000000000000000}.

$$\frac{\frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000}}{72\times \frac{1}{10000000000000000000000000000000000000000}\times 4805}$$

Multiplica 72 y \frac{1}{10000000000000000000000000000000000000000} para obtener \frac{9}{1250000000000000000000000000000000000000}.

$$\frac{\frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000}}{\frac{9}{1250000000000000000000000000000000000000}\times 4805}$$

Multiplica \frac{9}{1250000000000000000000000000000000000000} y 4805 para obtener \frac{8649}{250000000000000000000000000000000000000}.

$$\frac{\frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000}}{\frac{8649}{250000000000000000000000000000000000000}}$$

Divide \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000} por \frac{8649}{250000000000000000000000000000000000000} al multiplicar \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000} por el recíproco de \frac{8649}{250000000000000000000000000000000000000}.

$$\frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000}\times \frac{250000000000000000000000000000000000000}{8649}$$

Multiplica \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000} y \frac{250000000000000000000000000000000000000}{8649} para obtener \frac{881721}{24025000000000000000000000000000}.

$$\frac{881721}{24025000000000000000000000000000}$$

Factorizar

$$\frac{3 ^ {2} \cdot 313 ^ {2}}{2 ^ {27} \cdot 5 ^ {29} \cdot 31 ^ {2}} = 3,6700145681581686 \times 10^{-26}$$