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

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

تقييم

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

خطوات الحل

لضرب الأسس الخاصة بنفس الأساس، أضف القيم الخاصة بها. اجمع -31 مع -9 للحصول على -40.

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

احسب 3 بالأس 2 لتحصل على 9.

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

اضرب 6 في 626 لتحصل على 3756.

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

احسب 10 بالأس -34 لتحصل على \frac{1}{10000000000000000000000000000000000}.

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

اضرب 3756 في \frac{1}{10000000000000000000000000000000000} لتحصل على \frac{939}{2500000000000000000000000000000000}.

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

احسب \frac{939}{2500000000000000000000000000000000} بالأس 2 لتحصل على \frac{881721}{6250000000000000000000000000000000000000000000000000000000000000000}.

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

اضرب 9 في \frac{881721}{6250000000000000000000000000000000000000000000000000000000000000000} لتحصل على \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000}.

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

اضرب 8 في 9 لتحصل على 72.

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

اضرب 72 في 1 لتحصل على 72.

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

احسب 10 بالأس -40 لتحصل على \frac{1}{10000000000000000000000000000000000000000}.

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

اضرب 72 في \frac{1}{10000000000000000000000000000000000000000} لتحصل على \frac{9}{1250000000000000000000000000000000000000}.

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

اضرب \frac{9}{1250000000000000000000000000000000000000} في 4805 لتحصل على \frac{8649}{250000000000000000000000000000000000000}.

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

اقسم \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000} على \frac{8649}{250000000000000000000000000000000000000} من خلال ضرب \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000} في مقلوب \frac{8649}{250000000000000000000000000000000000000}.

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

اضرب \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000} في \frac{250000000000000000000000000000000000000}{8649} لتحصل على \frac{881721}{24025000000000000000000000000000}.

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

تحليل العوامل

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