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

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

求值

$$\frac{881721}{24025000000000000000000000000000}\approx 3.670014568 \cdot 10^{-26}$$

求解步骤

同底的幂相乘，即将其指数相加。-31 加 -9 得 -40。

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

计算 2 的 3 乘方，得到 9。

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

将 6 与 626 相乘，得到 3756。

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

计算 -34 的 10 乘方，得到 \frac{1}{10000000000000000000000000000000000}。

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

将 3756 与 \frac{1}{10000000000000000000000000000000000} 相乘，得到 \frac{939}{2500000000000000000000000000000000}。

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

计算 2 的 \frac{939}{2500000000000000000000000000000000} 乘方，得到 \frac{881721}{6250000000000000000000000000000000000000000000000000000000000000000}。

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

将 9 与 \frac{881721}{6250000000000000000000000000000000000000000000000000000000000000000} 相乘，得到 \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000}。

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

将 8 与 9 相乘，得到 72。

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

将 72 与 1 相乘，得到 72。

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

计算 -40 的 10 乘方，得到 \frac{1}{10000000000000000000000000000000000000000}。

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

将 72 与 \frac{1}{10000000000000000000000000000000000000000} 相乘，得到 \frac{9}{1250000000000000000000000000000000000000}。

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

将 \frac{9}{1250000000000000000000000000000000000000} 与 4805 相乘，得到 \frac{8649}{250000000000000000000000000000000000000}。

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

\frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000} 除以 \frac{8649}{250000000000000000000000000000000000000} 的计算方法是用 \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000} 乘以 \frac{8649}{250000000000000000000000000000000000000} 的倒数。

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

将 \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000} 与 \frac{250000000000000000000000000000000000000}{8649} 相乘，得到 \frac{881721}{24025000000000000000000000000000}。

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

因式分解

$$\frac{3 ^ {2} \cdot 313 ^ {2}}{2 ^ {27} \cdot 5 ^ {29} \cdot 31 ^ {2}} = 3.6700145681581686 \times 10^{-26}$$