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

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

Изчисляване

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

Стъпки на решението

За да умножите степени с една и съща основа, съберете техните експоненти. Съберете -31 и -9, за да получите -40.

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

Изчислявате 2 на степен 3 и получавате 9.

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

Умножете 6 по 626, за да получите 3756.

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

Изчислявате -34 на степен 10 и получавате \frac{1}{10000000000000000000000000000000000}.

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

Умножете 3756 по \frac{1}{10000000000000000000000000000000000}, за да получите \frac{939}{2500000000000000000000000000000000}.

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

Изчислявате 2 на степен \frac{939}{2500000000000000000000000000000000} и получавате \frac{881721}{6250000000000000000000000000000000000000000000000000000000000000000}.

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

Умножете 9 по \frac{881721}{6250000000000000000000000000000000000000000000000000000000000000000}, за да получите \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000}.

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

Умножете 8 по 9, за да получите 72.

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

Умножете 72 по 1, за да получите 72.

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

Изчислявате -40 на степен 10 и получавате \frac{1}{10000000000000000000000000000000000000000}.

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

Умножете 72 по \frac{1}{10000000000000000000000000000000000000000}, за да получите \frac{9}{1250000000000000000000000000000000000000}.

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

Умножете \frac{9}{1250000000000000000000000000000000000000} по 4805, за да получите \frac{8649}{250000000000000000000000000000000000000}.

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

Разделете \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000} на \frac{8649}{250000000000000000000000000000000000000} чрез умножаване на \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000} по обратната стойност на \frac{8649}{250000000000000000000000000000000000000}.

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

Умножете \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000} по \frac{250000000000000000000000000000000000000}{8649}, за да получите \frac{881721}{24025000000000000000000000000000}.

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

Разлагане на множители

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