다음을 풀어보세요: frac{3^{2}*(6*626*10^-34)^2}{8*9*1*10^-31*(48.05*10^-9)}

$$\frac { 3 ^ { 2 } \times ( 6 \cdot 626 \times 10 ^ { - 34 } ) ^ { 2 } } { 8 \times 9 \cdot 1 \times 10 ^ { - 31 } \times ( 48.05 \times 10 ^ { - 9 } ) }$$

계산

$$\frac{881721}{240250000000000000000000000000}\approx 3.670014568 \cdot 10^{-24}$$

해답 단계

같은 기수의 제곱을 곱하려면 해당 지수를 더합니다. -31과(와) -9을(를) 더하여 -40을(를) 구합니다.

$$\frac{3^{2}\times \left(6\times 626\times 10^{-34}\right)^{2}}{8\times 9\times 1\times 10^{-40}\times 48.05}$$

3의 2제곱을 계산하여 9을(를) 구합니다.

$$\frac{9\times \left(6\times 626\times 10^{-34}\right)^{2}}{8\times 9\times 1\times 10^{-40}\times 48.05}$$

6과(와) 626을(를) 곱하여 3756(을)를 구합니다.

$$\frac{9\times \left(3756\times 10^{-34}\right)^{2}}{8\times 9\times 1\times 10^{-40}\times 48.05}$$

10의 -34제곱을 계산하여 \frac{1}{10000000000000000000000000000000000}을(를) 구합니다.

$$\frac{9\times \left(3756\times \frac{1}{10000000000000000000000000000000000}\right)^{2}}{8\times 9\times 1\times 10^{-40}\times 48.05}$$

3756과(와) \frac{1}{10000000000000000000000000000000000}을(를) 곱하여 \frac{939}{2500000000000000000000000000000000}(을)를 구합니다.

$$\frac{9\times \left(\frac{939}{2500000000000000000000000000000000}\right)^{2}}{8\times 9\times 1\times 10^{-40}\times 48.05}$$

\frac{939}{2500000000000000000000000000000000}의 2제곱을 계산하여 \frac{881721}{6250000000000000000000000000000000000000000000000000000000000000000}을(를) 구합니다.

$$\frac{9\times \frac{881721}{6250000000000000000000000000000000000000000000000000000000000000000}}{8\times 9\times 1\times 10^{-40}\times 48.05}$$

9과(와) \frac{881721}{6250000000000000000000000000000000000000000000000000000000000000000}을(를) 곱하여 \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000}(을)를 구합니다.

$$\frac{\frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000}}{8\times 9\times 1\times 10^{-40}\times 48.05}$$

8과(와) 9을(를) 곱하여 72(을)를 구합니다.

$$\frac{\frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000}}{72\times 1\times 10^{-40}\times 48.05}$$

72과(와) 1을(를) 곱하여 72(을)를 구합니다.

$$\frac{\frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000}}{72\times 10^{-40}\times 48.05}$$

10의 -40제곱을 계산하여 \frac{1}{10000000000000000000000000000000000000000}을(를) 구합니다.

$$\frac{\frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000}}{72\times \frac{1}{10000000000000000000000000000000000000000}\times 48.05}$$

72과(와) \frac{1}{10000000000000000000000000000000000000000}을(를) 곱하여 \frac{9}{1250000000000000000000000000000000000000}(을)를 구합니다.

$$\frac{\frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000}}{\frac{9}{1250000000000000000000000000000000000000}\times 48.05}$$

\frac{9}{1250000000000000000000000000000000000000}과(와) 48.05을(를) 곱하여 \frac{8649}{25000000000000000000000000000000000000000}(을)를 구합니다.

$$\frac{\frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000}}{\frac{8649}{25000000000000000000000000000000000000000}}$$

\frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000}에 \frac{8649}{25000000000000000000000000000000000000000}의 역수를 곱하여 \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000}을(를) \frac{8649}{25000000000000000000000000000000000000000}(으)로 나눕니다.

$$\frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000}\times \frac{25000000000000000000000000000000000000000}{8649}$$

\frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000}과(와) \frac{25000000000000000000000000000000000000000}{8649}을(를) 곱하여 \frac{881721}{240250000000000000000000000000}(을)를 구합니다.

$$\frac{881721}{240250000000000000000000000000}$$

인수 분해

$$\frac{3 ^ {2} \cdot 313 ^ {2}}{2 ^ {25} \cdot 5 ^ {27} \cdot 31 ^ {2}} = 3.670014568158169 \times 10^{-24}$$