Solve 1.39*10^-3*24^-15*2/sqrt{2*pi*4*10^-15*2}

$$\frac { 1.39 \times 10 ^ { - 3 } \times 24 ^ { - 15 } \times 2 } { \sqrt { 2 } \times \pi \times 4 \times 10 ^ { - 15 } \times 2 }$$

Evaluate

$$\frac{1357421875\sqrt{2}}{3944197523094110208\pi }\approx 1.549249315 \cdot 10^{-10}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{1.39\times 10^{-3}\times 24^{-15}}{4\pi \sqrt{2}\times 10^{-15}}$$

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

$$\frac{1.39\times 10^{12}\times 24^{-15}}{4\pi \sqrt{2}}$$

Calculate 10 to the power of 12 and get 1000000000000.

$$\frac{1.39\times 1000000000000\times 24^{-15}}{4\pi \sqrt{2}}$$

Multiply 1.39 and 1000000000000 to get 1390000000000.

$$\frac{1390000000000\times 24^{-15}}{4\pi \sqrt{2}}$$

Calculate 24 to the power of -15 and get \frac{1}{504857282956046106624}.

$$\frac{1390000000000\times \frac{1}{504857282956046106624}}{4\pi \sqrt{2}}$$

Multiply 1390000000000 and \frac{1}{504857282956046106624} to get \frac{1357421875}{493024690386763776}.

$$\frac{\frac{1357421875}{493024690386763776}}{4\pi \sqrt{2}}$$

Rationalize the denominator of \frac{\frac{1357421875}{493024690386763776}}{4\pi \sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\frac{1357421875}{493024690386763776}\sqrt{2}}{4\pi \left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\frac{1357421875}{493024690386763776}\sqrt{2}}{4\pi \times 2}$$

Multiply 4 and 2 to get 8.

$$\frac{\frac{1357421875}{493024690386763776}\sqrt{2}}{8\pi }$$