Solve 1.3810^-23293.15/0.7*4pisqrt{2left(1.5510^-10right)^2}

$$\frac{ 1.38 { 10 }^{ -23 } 293.15 }{ 0.7 \cdot 4 \pi \sqrt{ 2 } { \left(1.55 { 10 }^{ -10 } \right) }^{ 2 } }$$

Evaluate

$$\frac{404547\sqrt{2}}{13454000\pi }\approx 0.013535761$$

Solution Steps

Calculate 10 to the power of -23 and get \frac{1}{100000000000000000000000}.

$$\frac{1.38\times \frac{1}{100000000000000000000000}\times 293.15}{0.7\times 4\pi \sqrt{2}\times \left(1.55\times 10^{-10}\right)^{2}}$$

Multiply 1.38 and \frac{1}{100000000000000000000000} to get \frac{69}{5000000000000000000000000}.

$$\frac{\frac{69}{5000000000000000000000000}\times 293.15}{0.7\times 4\pi \sqrt{2}\times \left(1.55\times 10^{-10}\right)^{2}}$$

Multiply \frac{69}{5000000000000000000000000} and 293.15 to get \frac{404547}{100000000000000000000000000}.

$$\frac{\frac{404547}{100000000000000000000000000}}{0.7\times 4\pi \sqrt{2}\times \left(1.55\times 10^{-10}\right)^{2}}$$

Multiply 0.7 and 4 to get 2.8.

$$\frac{\frac{404547}{100000000000000000000000000}}{2.8\pi \sqrt{2}\times \left(1.55\times 10^{-10}\right)^{2}}$$

Calculate 10 to the power of -10 and get \frac{1}{10000000000}.

$$\frac{\frac{404547}{100000000000000000000000000}}{2.8\pi \sqrt{2}\times \left(1.55\times \frac{1}{10000000000}\right)^{2}}$$

Multiply 1.55 and \frac{1}{10000000000} to get \frac{31}{200000000000}.

$$\frac{\frac{404547}{100000000000000000000000000}}{2.8\pi \sqrt{2}\times \left(\frac{31}{200000000000}\right)^{2}}$$

Calculate \frac{31}{200000000000} to the power of 2 and get \frac{961}{40000000000000000000000}.

$$\frac{\frac{404547}{100000000000000000000000000}}{2.8\pi \sqrt{2}\times \frac{961}{40000000000000000000000}}$$

Multiply 2.8 and \frac{961}{40000000000000000000000} to get \frac{6727}{100000000000000000000000}.

$$\frac{\frac{404547}{100000000000000000000000000}}{\frac{6727}{100000000000000000000000}\pi \sqrt{2}}$$

Rationalize the denominator of \frac{\frac{404547}{100000000000000000000000000}}{\frac{6727}{100000000000000000000000}\pi \sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\frac{404547}{100000000000000000000000000}\sqrt{2}}{\frac{6727}{100000000000000000000000}\pi \left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\frac{404547}{100000000000000000000000000}\sqrt{2}}{\frac{6727}{100000000000000000000000}\pi \times 2}$$

Multiply \frac{6727}{100000000000000000000000} and 2 to get \frac{6727}{50000000000000000000000}.

$$\frac{\frac{404547}{100000000000000000000000000}\sqrt{2}}{\frac{6727}{50000000000000000000000}\pi }$$