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

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

Auswerten

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

Lösungsschritte

Um Potenzen mit derselben Basis zu multiplizieren, addieren Sie ihre Exponenten. Addieren Sie -31 und -9, um -40 zu erhalten.

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

Potenzieren Sie 3 mit 2, und erhalten Sie 9.

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

Multiplizieren Sie 6 und 626, um 3756 zu erhalten.

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

Potenzieren Sie 10 mit -34, und erhalten Sie \frac{1}{10000000000000000000000000000000000}.

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

Multiplizieren Sie 3756 und \frac{1}{10000000000000000000000000000000000}, um \frac{939}{2500000000000000000000000000000000} zu erhalten.

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

Potenzieren Sie \frac{939}{2500000000000000000000000000000000} mit 2, und erhalten Sie \frac{881721}{6250000000000000000000000000000000000000000000000000000000000000000}.

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

Multiplizieren Sie 9 und \frac{881721}{6250000000000000000000000000000000000000000000000000000000000000000}, um \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000} zu erhalten.

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

Multiplizieren Sie 8 und 9, um 72 zu erhalten.

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

Multiplizieren Sie 72 und 1, um 72 zu erhalten.

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

Potenzieren Sie 10 mit -40, und erhalten Sie \frac{1}{10000000000000000000000000000000000000000}.

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

Multiplizieren Sie 72 und \frac{1}{10000000000000000000000000000000000000000}, um \frac{9}{1250000000000000000000000000000000000000} zu erhalten.

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

Multiplizieren Sie \frac{9}{1250000000000000000000000000000000000000} und 4805, um \frac{8649}{250000000000000000000000000000000000000} zu erhalten.

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

Dividieren Sie \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000} durch \frac{8649}{250000000000000000000000000000000000000}, indem Sie \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000} mit dem Kehrwert von \frac{8649}{250000000000000000000000000000000000000} multiplizieren.

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

Multiplizieren Sie \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000} und \frac{250000000000000000000000000000000000000}{8649}, um \frac{881721}{24025000000000000000000000000000} zu erhalten.

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

Faktorisieren

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