Solve 2*13^4*48*47/(52*51*50*49*48*47)frac{1{6*5*4*3*1}}

$$\frac{ 2 \times { 13 }^{ 4 } \times 48 \times 47 }{ (52 \times 51 \times 50 \times 49 \times 48 \times 47) \frac{ 1 }{ 6 \times 5 \times 4 \times 3 \times 1 } }$$

Evaluate

$$\frac{13182}{4165}\approx 3.164945978$$

Solution Steps

Calculate 13 to the power of 4 and get 28561.

$$\frac{2\times 28561\times 48\times 47}{52\times 51\times 50\times 49\times 48\times 47\times \frac{1}{6\times 5\times 4\times 3\times 1}}$$

Multiply 2 and 28561 to get 57122.

$$\frac{57122\times 48\times 47}{52\times 51\times 50\times 49\times 48\times 47\times \frac{1}{6\times 5\times 4\times 3\times 1}}$$

Multiply 57122 and 48 to get 2741856.

$$\frac{2741856\times 47}{52\times 51\times 50\times 49\times 48\times 47\times \frac{1}{6\times 5\times 4\times 3\times 1}}$$

Multiply 2741856 and 47 to get 128867232.

$$\frac{128867232}{52\times 51\times 50\times 49\times 48\times 47\times \frac{1}{6\times 5\times 4\times 3\times 1}}$$

Multiply 52 and 51 to get 2652.

$$\frac{128867232}{2652\times 50\times 49\times 48\times 47\times \frac{1}{6\times 5\times 4\times 3\times 1}}$$

Multiply 2652 and 50 to get 132600.

$$\frac{128867232}{132600\times 49\times 48\times 47\times \frac{1}{6\times 5\times 4\times 3\times 1}}$$

Multiply 132600 and 49 to get 6497400.

$$\frac{128867232}{6497400\times 48\times 47\times \frac{1}{6\times 5\times 4\times 3\times 1}}$$

Multiply 6497400 and 48 to get 311875200.

$$\frac{128867232}{311875200\times 47\times \frac{1}{6\times 5\times 4\times 3\times 1}}$$

Multiply 311875200 and 47 to get 14658134400.

$$\frac{128867232}{14658134400\times \frac{1}{6\times 5\times 4\times 3\times 1}}$$

Multiply 6 and 5 to get 30.

$$\frac{128867232}{14658134400\times \frac{1}{30\times 4\times 3\times 1}}$$

Multiply 30 and 4 to get 120.

$$\frac{128867232}{14658134400\times \frac{1}{120\times 3\times 1}}$$

Multiply 120 and 3 to get 360.

$$\frac{128867232}{14658134400\times \frac{1}{360\times 1}}$$

Multiply 360 and 1 to get 360.

$$\frac{128867232}{14658134400\times \frac{1}{360}}$$

Multiply 14658134400 and \frac{1}{360} to get \frac{14658134400}{360}.

$$\frac{128867232}{\frac{14658134400}{360}}$$

Divide 14658134400 by 360 to get 40717040.

$$\frac{128867232}{40717040}$$

Reduce the fraction \frac{128867232}{40717040} to lowest terms by extracting and canceling out 9776.

$$\frac{13182}{4165}$$

Factor

$$\frac{2 \cdot 3 \cdot 13 ^ {3}}{5 \cdot 7 ^ {2} \cdot 17} = 3\frac{687}{4165} = 3.1649459783913567$$