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

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

Évaluer

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

Étapes de la solution

Pour multiplier les puissances de la même base, additionnez leurs exposants. Additionnez -31 et -9 pour obtenir -40.

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

Calculer 3 à la puissance 2 et obtenir 9.

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

Multiplier 6 et 626 pour obtenir 3756.

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

Calculer 10 à la puissance -34 et obtenir \frac{1}{10000000000000000000000000000000000}.

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

Multiplier 3756 et \frac{1}{10000000000000000000000000000000000} pour obtenir \frac{939}{2500000000000000000000000000000000}.

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

Calculer \frac{939}{2500000000000000000000000000000000} à la puissance 2 et obtenir \frac{881721}{6250000000000000000000000000000000000000000000000000000000000000000}.

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

Multiplier 9 et \frac{881721}{6250000000000000000000000000000000000000000000000000000000000000000} pour obtenir \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000}.

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

Multiplier 8 et 9 pour obtenir 72.

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

Multiplier 72 et 1 pour obtenir 72.

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

Calculer 10 à la puissance -40 et obtenir \frac{1}{10000000000000000000000000000000000000000}.

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

Multiplier 72 et \frac{1}{10000000000000000000000000000000000000000} pour obtenir \frac{9}{1250000000000000000000000000000000000000}.

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

Multiplier \frac{9}{1250000000000000000000000000000000000000} et 4805 pour obtenir \frac{8649}{250000000000000000000000000000000000000}.

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

Diviser \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000} par \frac{8649}{250000000000000000000000000000000000000} en multipliant \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000} par la réciproque de \frac{8649}{250000000000000000000000000000000000000}.

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

Multiplier \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000} et \frac{250000000000000000000000000000000000000}{8649} pour obtenir \frac{881721}{24025000000000000000000000000000}.

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

Factoriser

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