Solve {left(frac{8*10^-6/2piright)}^2}{28*10^-3}

$$\frac{ { \left( \frac{ 8 \times { 10 }^{ -6 } }{ 2 \pi } \right) }^{ 2 } }{ 28 \times { 10 }^{ -3 } }$$

Evaluate

$$\frac{1}{1750000000\pi ^{2}}\approx 5.789781922 \cdot 10^{-11}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{\left(\frac{4\times 10^{-6}}{\pi }\right)^{2}}{28\times 10^{-3}}$$

Calculate 10 to the power of -6 and get \frac{1}{1000000}.

$$\frac{\left(\frac{4\times \frac{1}{1000000}}{\pi }\right)^{2}}{28\times 10^{-3}}$$

Multiply 4 and \frac{1}{1000000} to get \frac{1}{250000}.

$$\frac{\left(\frac{\frac{1}{250000}}{\pi }\right)^{2}}{28\times 10^{-3}}$$

Express \frac{\frac{1}{250000}}{\pi } as a single fraction.

$$\frac{\left(\frac{1}{250000\pi }\right)^{2}}{28\times 10^{-3}}$$

To raise \frac{1}{250000\pi } to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\frac{1^{2}}{\left(250000\pi \right)^{2}}}{28\times 10^{-3}}$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$\frac{\frac{1^{2}}{\left(250000\pi \right)^{2}}}{28\times \frac{1}{1000}}$$

Multiply 28 and \frac{1}{1000} to get \frac{7}{250}.

$$\frac{\frac{1^{2}}{\left(250000\pi \right)^{2}}}{\frac{7}{250}}$$

Divide \frac{1^{2}}{\left(250000\pi \right)^{2}} by \frac{7}{250} by multiplying \frac{1^{2}}{\left(250000\pi \right)^{2}} by the reciprocal of \frac{7}{250}.

$$\frac{1^{2}\times 250}{\left(250000\pi \right)^{2}\times 7}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{1\times 250}{\left(250000\pi \right)^{2}\times 7}$$

Multiply 1 and 250 to get 250.

$$\frac{250}{\left(250000\pi \right)^{2}\times 7}$$

Expand \left(250000\pi \right)^{2}.

$$\frac{250}{250000^{2}\pi ^{2}\times 7}$$

Calculate 250000 to the power of 2 and get 62500000000.

$$\frac{250}{62500000000\pi ^{2}\times 7}$$

Multiply 62500000000 and 7 to get 437500000000.

$$\frac{250}{437500000000\pi ^{2}}$$

Expand

$$\frac{1}{1750000000 \pi ^ {2}} = 5.789781922419302 \times 10^{-11}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{\left(\frac{4\times 10^{-6}}{\pi }\right)^{2}}{28\times 10^{-3}}$$

Calculate 10 to the power of -6 and get \frac{1}{1000000}.

$$\frac{\left(\frac{4\times \frac{1}{1000000}}{\pi }\right)^{2}}{28\times 10^{-3}}$$

Multiply 4 and \frac{1}{1000000} to get \frac{1}{250000}.

$$\frac{\left(\frac{\frac{1}{250000}}{\pi }\right)^{2}}{28\times 10^{-3}}$$

Express \frac{\frac{1}{250000}}{\pi } as a single fraction.

$$\frac{\left(\frac{1}{250000\pi }\right)^{2}}{28\times 10^{-3}}$$

To raise \frac{1}{250000\pi } to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\frac{1^{2}}{\left(250000\pi \right)^{2}}}{28\times 10^{-3}}$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$\frac{\frac{1^{2}}{\left(250000\pi \right)^{2}}}{28\times \frac{1}{1000}}$$

Multiply 28 and \frac{1}{1000} to get \frac{7}{250}.

$$\frac{\frac{1^{2}}{\left(250000\pi \right)^{2}}}{\frac{7}{250}}$$

Divide \frac{1^{2}}{\left(250000\pi \right)^{2}} by \frac{7}{250} by multiplying \frac{1^{2}}{\left(250000\pi \right)^{2}} by the reciprocal of \frac{7}{250}.

$$\frac{1^{2}\times 250}{\left(250000\pi \right)^{2}\times 7}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{1\times 250}{\left(250000\pi \right)^{2}\times 7}$$

Multiply 1 and 250 to get 250.

$$\frac{250}{\left(250000\pi \right)^{2}\times 7}$$

Expand \left(250000\pi \right)^{2}.

$$\frac{250}{250000^{2}\pi ^{2}\times 7}$$

Calculate 250000 to the power of 2 and get 62500000000.

$$\frac{250}{62500000000\pi ^{2}\times 7}$$

Multiply 62500000000 and 7 to get 437500000000.

$$\frac{250}{437500000000\pi ^{2}}$$