Solve 1/64*pi*(50*10^-3)^4/(frac{10{2}*10^-3)^2*pi}

$$\frac { \frac { 1 } { 64 \times \pi \times ( 50 \times 10 ^ { - 3 } ) ^ { 4 } } } { ( \frac { 10 } { 2 } \times 10 ^ { - 3 } ) ^ { 2 } \times \pi }$$

Evaluate

$$\frac{100000000}{\pi ^{2}}\approx 10132118.364233777$$

Solution Steps

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

$$\frac{\frac{1}{64\pi \times \left(50\times \frac{1}{1000}\right)^{4}}}{\left(\frac{10}{2}\times 10^{-3}\right)^{2}\pi }$$

Multiply 50 and \frac{1}{1000} to get \frac{1}{20}.

$$\frac{\frac{1}{64\pi \times \left(\frac{1}{20}\right)^{4}}}{\left(\frac{10}{2}\times 10^{-3}\right)^{2}\pi }$$

Calculate \frac{1}{20} to the power of 4 and get \frac{1}{160000}.

$$\frac{\frac{1}{64\pi \times \frac{1}{160000}}}{\left(\frac{10}{2}\times 10^{-3}\right)^{2}\pi }$$

Multiply 64 and \frac{1}{160000} to get \frac{1}{2500}.

$$\frac{\frac{1}{\frac{1}{2500}\pi }}{\left(\frac{10}{2}\times 10^{-3}\right)^{2}\pi }$$

Divide 10 by 2 to get 5.

$$\frac{\frac{1}{\frac{1}{2500}\pi }}{\left(5\times 10^{-3}\right)^{2}\pi }$$

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

$$\frac{\frac{1}{\frac{1}{2500}\pi }}{\left(5\times \frac{1}{1000}\right)^{2}\pi }$$

Multiply 5 and \frac{1}{1000} to get \frac{1}{200}.

$$\frac{\frac{1}{\frac{1}{2500}\pi }}{\left(\frac{1}{200}\right)^{2}\pi }$$

Calculate \frac{1}{200} to the power of 2 and get \frac{1}{40000}.

$$\frac{\frac{1}{\frac{1}{2500}\pi }}{\frac{1}{40000}\pi }$$

Express \frac{\frac{1}{\frac{1}{2500}\pi }}{\frac{1}{40000}\pi } as a single fraction.

$$\frac{1}{\frac{1}{2500}\pi \times \frac{1}{40000}\pi }$$

Multiply \pi and \pi to get \pi ^{2}.

$$\frac{1}{\frac{1}{2500}\pi ^{2}\times \frac{1}{40000}}$$

Multiply \frac{1}{2500} and \frac{1}{40000} to get \frac{1}{100000000}.

$$\frac{1}{\frac{1}{100000000}\pi ^{2}}$$

Expand

$$\frac{100000000}{\pi ^ {2}} = 10132118.364233777$$

Solution Steps

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

$$\frac{\frac{1}{64\pi \times \left(50\times \frac{1}{1000}\right)^{4}}}{\left(\frac{10}{2}\times 10^{-3}\right)^{2}\pi }$$

Multiply 50 and \frac{1}{1000} to get \frac{1}{20}.

$$\frac{\frac{1}{64\pi \times \left(\frac{1}{20}\right)^{4}}}{\left(\frac{10}{2}\times 10^{-3}\right)^{2}\pi }$$

Calculate \frac{1}{20} to the power of 4 and get \frac{1}{160000}.

$$\frac{\frac{1}{64\pi \times \frac{1}{160000}}}{\left(\frac{10}{2}\times 10^{-3}\right)^{2}\pi }$$

Multiply 64 and \frac{1}{160000} to get \frac{1}{2500}.

$$\frac{\frac{1}{\frac{1}{2500}\pi }}{\left(\frac{10}{2}\times 10^{-3}\right)^{2}\pi }$$

Divide 10 by 2 to get 5.

$$\frac{\frac{1}{\frac{1}{2500}\pi }}{\left(5\times 10^{-3}\right)^{2}\pi }$$

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

$$\frac{\frac{1}{\frac{1}{2500}\pi }}{\left(5\times \frac{1}{1000}\right)^{2}\pi }$$

Multiply 5 and \frac{1}{1000} to get \frac{1}{200}.

$$\frac{\frac{1}{\frac{1}{2500}\pi }}{\left(\frac{1}{200}\right)^{2}\pi }$$

Calculate \frac{1}{200} to the power of 2 and get \frac{1}{40000}.

$$\frac{\frac{1}{\frac{1}{2500}\pi }}{\frac{1}{40000}\pi }$$

Express \frac{\frac{1}{\frac{1}{2500}\pi }}{\frac{1}{40000}\pi } as a single fraction.

$$\frac{1}{\frac{1}{2500}\pi \times \frac{1}{40000}\pi }$$

Multiply \pi and \pi to get \pi ^{2}.

$$\frac{1}{\frac{1}{2500}\pi ^{2}\times \frac{1}{40000}}$$

Multiply \frac{1}{2500} and \frac{1}{40000} to get \frac{1}{100000000}.

$$\frac{1}{\frac{1}{100000000}\pi ^{2}}$$