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

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

შეფასება

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

ამონახსნის ეტაპები

იმავე ფუძის ჯერადი რიცხვების გასამრავლებლად, შეკრიბეთ მათი ექსპონენტები. შეკრიბეთ -31 და -9 რომ მიიღოთ -40.

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

გამოთვალეთ2-ის 3 ხარისხი და მიიღეთ 9.

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

გადაამრავლეთ 6 და 626, რათა მიიღოთ 3756.

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

გამოთვალეთ-34-ის 10 ხარისხი და მიიღეთ \frac{1}{10000000000000000000000000000000000}.

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

გადაამრავლეთ 3756 და \frac{1}{10000000000000000000000000000000000}, რათა მიიღოთ \frac{939}{2500000000000000000000000000000000}.

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

გამოთვალეთ2-ის \frac{939}{2500000000000000000000000000000000} ხარისხი და მიიღეთ \frac{881721}{6250000000000000000000000000000000000000000000000000000000000000000}.

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

გადაამრავლეთ 9 და \frac{881721}{6250000000000000000000000000000000000000000000000000000000000000000}, რათა მიიღოთ \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000}.

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

გადაამრავლეთ 8 და 9, რათა მიიღოთ 72.

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

გადაამრავლეთ 72 და 1, რათა მიიღოთ 72.

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

გამოთვალეთ-40-ის 10 ხარისხი და მიიღეთ \frac{1}{10000000000000000000000000000000000000000}.

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

გადაამრავლეთ 72 და \frac{1}{10000000000000000000000000000000000000000}, რათა მიიღოთ \frac{9}{1250000000000000000000000000000000000000}.

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

გადაამრავლეთ \frac{9}{1250000000000000000000000000000000000000} და 4805, რათა მიიღოთ \frac{8649}{250000000000000000000000000000000000000}.

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

გაყავით \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000} \frac{8649}{250000000000000000000000000000000000000}-ზე \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000}-ის გამრავლებით \frac{8649}{250000000000000000000000000000000000000}-ის შექცეულ სიდიდეზე.

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

გადაამრავლეთ \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000} და \frac{250000000000000000000000000000000000000}{8649}, რათა მიიღოთ \frac{881721}{24025000000000000000000000000000}.

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

მამრავლი

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