求解 frac{9*10^{8}*(1.6*10^{-19})^2}{6.67*10^-11*9.1*10^-31*1.66*10^-27}

$$\frac { 9 \times 10 ^ { 8 } \times ( 1.6 \times 10 ^ { - 19 } ) ^ { 2 } } { 6.67 \times 10 ^ { - 11 } \times 9.1 \times 10 ^ { - 31 } \times 1.66 \times 10 ^ { - 27 } }$$

求值

$$\frac{1152000000000000000000000000000000000000000000}{5037851}\approx 2.286689305 \cdot 10^{38}$$

求解步骤

同底的幂相乘，即将其指数相加。-11 加 -31 得 -42。

$$\frac{9\times 10^{8}\times \left(1.6\times 10^{-19}\right)^{2}}{6.67\times 10^{-42}\times 9.1\times 1.66\times 10^{-27}}$$

同底的幂相乘，即将其指数相加。-42 加 -27 得 -69。

$$\frac{9\times 10^{8}\times \left(1.6\times 10^{-19}\right)^{2}}{6.67\times 10^{-69}\times 9.1\times 1.66}$$

底相同的幂相除，运算方法是底不变，指数为分子的指数减去分母的指数所得的值。

$$\frac{9\times 10^{77}\times \left(1.6\times 10^{-19}\right)^{2}}{1.66\times 6.67\times 9.1}$$

计算 77 的 10 乘方，得到 100000000000000000000000000000000000000000000000000000000000000000000000000000。

$$\frac{9\times 100000000000000000000000000000000000000000000000000000000000000000000000000000\times \left(1.6\times 10^{-19}\right)^{2}}{1.66\times 6.67\times 9.1}$$

将 9 与 100000000000000000000000000000000000000000000000000000000000000000000000000000 相乘，得到 900000000000000000000000000000000000000000000000000000000000000000000000000000。

$$\frac{900000000000000000000000000000000000000000000000000000000000000000000000000000\times \left(1.6\times 10^{-19}\right)^{2}}{1.66\times 6.67\times 9.1}$$

计算 -19 的 10 乘方，得到 \frac{1}{10000000000000000000}。

$$\frac{900000000000000000000000000000000000000000000000000000000000000000000000000000\times \left(1.6\times \frac{1}{10000000000000000000}\right)^{2}}{1.66\times 6.67\times 9.1}$$

将 1.6 与 \frac{1}{10000000000000000000} 相乘，得到 \frac{1}{6250000000000000000}。

$$\frac{900000000000000000000000000000000000000000000000000000000000000000000000000000\times \left(\frac{1}{6250000000000000000}\right)^{2}}{1.66\times 6.67\times 9.1}$$

计算 2 的 \frac{1}{6250000000000000000} 乘方，得到 \frac{1}{39062500000000000000000000000000000000}。

$$\frac{900000000000000000000000000000000000000000000000000000000000000000000000000000\times \frac{1}{39062500000000000000000000000000000000}}{1.66\times 6.67\times 9.1}$$

将 900000000000000000000000000000000000000000000000000000000000000000000000000000 与 \frac{1}{39062500000000000000000000000000000000} 相乘，得到 23040000000000000000000000000000000000000。

$$\frac{23040000000000000000000000000000000000000}{1.66\times 6.67\times 9.1}$$

将 1.66 与 6.67 相乘，得到 11.0722。

$$\frac{23040000000000000000000000000000000000000}{11.0722\times 9.1}$$

将 11.0722 与 9.1 相乘，得到 100.75702。

$$\frac{23040000000000000000000000000000000000000}{100.75702}$$

将分子和分母同时乘以 100000 以展开 \frac{23040000000000000000000000000000000000000}{100.75702}。

$$\frac{2304000000000000000000000000000000000000000000}{10075702}$$

通过求根和消去 2，将分数 \frac{2304000000000000000000000000000000000000000000}{10075702} 降低为最简分数。

$$\frac{1152000000000000000000000000000000000000000000}{5037851}$$

因式分解

$$\frac{2 ^ {49} \cdot 3 ^ {2} \cdot 5 ^ {42}}{7 \cdot 13 \cdot 23 \cdot 29 \cdot 83} = 2.2866893046261194 \times 10^{38}\frac{983904}{5037851} = 2.2866893046261194 \times 10^{38}$$