Solve 1/4*79.4*3.14*1000*3.14/32*45^4/180*1000

$$\frac{ \frac{ 1 }{ 4 } \times 79.4 \times 3.14 \times 1000 \times \frac { 3.14 } { 32 } \times { 45 }^{ 4 } }{ 180 \times 1000 }$$

Evaluate

$$139330.87962890625$$

Solution Steps

Convert decimal number 79.4 to fraction \frac{794}{10}. Reduce the fraction \frac{794}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{1}{4}\times \frac{397}{5}\times 3.14\times 1000\times \frac{3.14}{32}\times 45^{4}}{180\times 1000}$$

Multiply \frac{1}{4} times \frac{397}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1\times 397}{4\times 5}\times 3.14\times 1000\times \frac{3.14}{32}\times 45^{4}}{180\times 1000}$$

Do the multiplications in the fraction \frac{1\times 397}{4\times 5}.

$$\frac{\frac{397}{20}\times 3.14\times 1000\times \frac{3.14}{32}\times 45^{4}}{180\times 1000}$$

Convert decimal number 3.14 to fraction \frac{314}{100}. Reduce the fraction \frac{314}{100} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{397}{20}\times \frac{157}{50}\times 1000\times \frac{3.14}{32}\times 45^{4}}{180\times 1000}$$

Multiply \frac{397}{20} times \frac{157}{50} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{397\times 157}{20\times 50}\times 1000\times \frac{3.14}{32}\times 45^{4}}{180\times 1000}$$

Do the multiplications in the fraction \frac{397\times 157}{20\times 50}.

$$\frac{\frac{62329}{1000}\times 1000\times \frac{3.14}{32}\times 45^{4}}{180\times 1000}$$

Cancel out 1000 and 1000.

$$\frac{62329\times \frac{3.14}{32}\times 45^{4}}{180\times 1000}$$

Expand \frac{3.14}{32} by multiplying both numerator and the denominator by 100.

$$\frac{62329\times \frac{314}{3200}\times 45^{4}}{180\times 1000}$$

Reduce the fraction \frac{314}{3200} to lowest terms by extracting and canceling out 2.

$$\frac{62329\times \frac{157}{1600}\times 45^{4}}{180\times 1000}$$

Express 62329\times \frac{157}{1600} as a single fraction.

$$\frac{\frac{62329\times 157}{1600}\times 45^{4}}{180\times 1000}$$

Multiply 62329 and 157 to get 9785653.

$$\frac{\frac{9785653}{1600}\times 45^{4}}{180\times 1000}$$

Calculate 45 to the power of 4 and get 4100625.

$$\frac{\frac{9785653}{1600}\times 4100625}{180\times 1000}$$

Express \frac{9785653}{1600}\times 4100625 as a single fraction.

$$\frac{\frac{9785653\times 4100625}{1600}}{180\times 1000}$$

Multiply 9785653 and 4100625 to get 40127293333125.

$$\frac{\frac{40127293333125}{1600}}{180\times 1000}$$

Reduce the fraction \frac{40127293333125}{1600} to lowest terms by extracting and canceling out 25.

$$\frac{\frac{1605091733325}{64}}{180\times 1000}$$

Multiply 180 and 1000 to get 180000.

$$\frac{\frac{1605091733325}{64}}{180000}$$

Express \frac{\frac{1605091733325}{64}}{180000} as a single fraction.

$$\frac{1605091733325}{64\times 180000}$$

Multiply 64 and 180000 to get 11520000.

$$\frac{1605091733325}{11520000}$$

Reduce the fraction \frac{1605091733325}{11520000} to lowest terms by extracting and canceling out 225.

$$\frac{7133741037}{51200}$$

Factor

$$\frac{397 \cdot 3 ^ {6} \cdot 157 ^ {2}}{2 ^ {11} \cdot 5 ^ {2}} = 139330\frac{45037}{51200} = 139330.87962890626$$