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

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

Evaluați

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

Pașii soluției

Pentru a înmulți puterile cu aceeași baze, adunați exponenții lor. Adunați -31 și -9 pentru a obține -40.

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

Calculați 3 la puterea 2 și obțineți 9.

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

Înmulțiți 6 cu 626 pentru a obține 3756.

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

Calculați 10 la puterea -34 și obțineți \frac{1}{10000000000000000000000000000000000}.

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

Înmulțiți 3756 cu \frac{1}{10000000000000000000000000000000000} pentru a obține \frac{939}{2500000000000000000000000000000000}.

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

Calculați \frac{939}{2500000000000000000000000000000000} la puterea 2 și obțineți \frac{881721}{6250000000000000000000000000000000000000000000000000000000000000000}.

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

Înmulțiți 9 cu \frac{881721}{6250000000000000000000000000000000000000000000000000000000000000000} pentru a obține \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000}.

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

Înmulțiți 8 cu 9 pentru a obține 72.

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

Înmulțiți 72 cu 1 pentru a obține 72.

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

Calculați 10 la puterea -40 și obțineți \frac{1}{10000000000000000000000000000000000000000}.

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

Înmulțiți 72 cu \frac{1}{10000000000000000000000000000000000000000} pentru a obține \frac{9}{1250000000000000000000000000000000000000}.

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

Înmulțiți \frac{9}{1250000000000000000000000000000000000000} cu 4805 pentru a obține \frac{8649}{250000000000000000000000000000000000000}.

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

Împărțiți \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000} la \frac{8649}{250000000000000000000000000000000000000} înmulțind pe \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000} cu reciproca lui \frac{8649}{250000000000000000000000000000000000000}.

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

Înmulțiți \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000} cu \frac{250000000000000000000000000000000000000}{8649} pentru a obține \frac{881721}{24025000000000000000000000000000}.

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

Descompunere în factori

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