Solve 1.38*10^-23*27.15/sqrt{2*pi*(3.5*10^-10)^2*101*10^5}=

$$\frac { 1.38 \times 10 ^ { - 23 } \times 27.15 } { \sqrt { 2 } \times \pi \times ( 3.5 \times 10 ^ { - 10 } ) ^ { 2 } \times 101 \times 10 ^ { 5 } } =$$

Evaluate

$$\frac{37467\sqrt{2}}{247450000000000\pi }\approx 6.815953004 \cdot 10^{-11}$$

Solution Steps

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{1.38\times 27.15}{101\pi \sqrt{2}\times 10^{28}\times \left(3.5\times 10^{-10}\right)^{2}}$$

Multiply 1.38 and 27.15 to get 37.467.

$$\frac{37.467}{101\pi \sqrt{2}\times 10^{28}\times \left(3.5\times 10^{-10}\right)^{2}}$$

Calculate 10 to the power of 28 and get 10000000000000000000000000000.

$$\frac{37.467}{101\pi \sqrt{2}\times 10000000000000000000000000000\times \left(3.5\times 10^{-10}\right)^{2}}$$

Multiply 101 and 10000000000000000000000000000 to get 1010000000000000000000000000000.

$$\frac{37.467}{1010000000000000000000000000000\pi \sqrt{2}\times \left(3.5\times 10^{-10}\right)^{2}}$$

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

$$\frac{37.467}{1010000000000000000000000000000\pi \sqrt{2}\times \left(3.5\times \frac{1}{10000000000}\right)^{2}}$$

Multiply 3.5 and \frac{1}{10000000000} to get \frac{7}{20000000000}.

$$\frac{37.467}{1010000000000000000000000000000\pi \sqrt{2}\times \left(\frac{7}{20000000000}\right)^{2}}$$

Calculate \frac{7}{20000000000} to the power of 2 and get \frac{49}{400000000000000000000}.

$$\frac{37.467}{1010000000000000000000000000000\pi \sqrt{2}\times \frac{49}{400000000000000000000}}$$

Multiply 1010000000000000000000000000000 and \frac{49}{400000000000000000000} to get 123725000000.

$$\frac{37.467}{123725000000\pi \sqrt{2}}$$

Rationalize the denominator of \frac{37.467}{123725000000\pi \sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{37.467\sqrt{2}}{123725000000\pi \left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{37.467\sqrt{2}}{123725000000\pi \times 2}$$

Multiply 123725000000 and 2 to get 247450000000.

$$\frac{37.467\sqrt{2}}{247450000000\pi }$$