Solve 138*10^-23*2715/sqrt{2*pi*(35*10^-10)^2*101*10^5}=

$$\frac { 138 \times 10 ^ { - 23 } \times 2715 } { \sqrt { 2 } \times \pi \times ( 35 \times 10 ^ { - 10 } ) ^ { 2 } \times 101 \times 10 ^ { 5 } } =$$

Evaluate

$$\frac{37467\sqrt{2}}{2474500000000\pi }\approx 6.815953004 \cdot 10^{-9}$$

Solution Steps

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

$$\frac{138\times 2715}{101\pi \sqrt{2}\times 10^{28}\times \left(35\times 10^{-10}\right)^{2}}$$

Multiply 138 and 2715 to get 374670.

$$\frac{374670}{101\pi \sqrt{2}\times 10^{28}\times \left(35\times 10^{-10}\right)^{2}}$$

Calculate 10 to the power of 28 and get 10000000000000000000000000000.

$$\frac{374670}{101\pi \sqrt{2}\times 10000000000000000000000000000\times \left(35\times 10^{-10}\right)^{2}}$$

Multiply 101 and 10000000000000000000000000000 to get 1010000000000000000000000000000.

$$\frac{374670}{1010000000000000000000000000000\pi \sqrt{2}\times \left(35\times 10^{-10}\right)^{2}}$$

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

$$\frac{374670}{1010000000000000000000000000000\pi \sqrt{2}\times \left(35\times \frac{1}{10000000000}\right)^{2}}$$

Multiply 35 and \frac{1}{10000000000} to get \frac{7}{2000000000}.

$$\frac{374670}{1010000000000000000000000000000\pi \sqrt{2}\times \left(\frac{7}{2000000000}\right)^{2}}$$

Calculate \frac{7}{2000000000} to the power of 2 and get \frac{49}{4000000000000000000}.

$$\frac{374670}{1010000000000000000000000000000\pi \sqrt{2}\times \frac{49}{4000000000000000000}}$$

Multiply 1010000000000000000000000000000 and \frac{49}{4000000000000000000} to get 12372500000000.

$$\frac{374670}{12372500000000\pi \sqrt{2}}$$

Rationalize the denominator of \frac{374670}{12372500000000\pi \sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{374670\sqrt{2}}{12372500000000\pi \left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{374670\sqrt{2}}{12372500000000\pi \times 2}$$

Cancel out 10 in both numerator and denominator.

$$\frac{37467\sqrt{2}}{2\times 1237250000000\pi }$$

Multiply 2 and 1237250000000 to get 2474500000000.

$$\frac{37467\sqrt{2}}{2474500000000\pi }$$