Solve 4*1/14^71000/frac{1000{41}+4118.2/147}

$$\frac{ 4 \cdot 1 }{ { 14 }^{ 7 } } \frac{ 1000 }{ \frac{ 1000 }{ 41 } +41 \frac{ 18.2 }{ 147 } }$$

Evaluate

$$\frac{76875}{132725954648}\approx 0.000000579$$

Solution Steps

Multiply 4 and 1 to get 4.

$$\frac{4}{14^{7}}\times \frac{1000}{\frac{1000}{41}+\frac{41\times 147+18.2}{147}}$$

Calculate 14 to the power of 7 and get 105413504.

$$\frac{4}{105413504}\times \frac{1000}{\frac{1000}{41}+\frac{41\times 147+18.2}{147}}$$

Reduce the fraction \frac{4}{105413504} to lowest terms by extracting and canceling out 4.

$$\frac{1}{26353376}\times \frac{1000}{\frac{1000}{41}+\frac{41\times 147+18.2}{147}}$$

Multiply 41 and 147 to get 6027.

$$\frac{1}{26353376}\times \frac{1000}{\frac{1000}{41}+\frac{6027+18.2}{147}}$$

Add 6027 and 18.2 to get 6045.2.

$$\frac{1}{26353376}\times \frac{1000}{\frac{1000}{41}+\frac{6045.2}{147}}$$

Expand \frac{6045.2}{147} by multiplying both numerator and the denominator by 10.

$$\frac{1}{26353376}\times \frac{1000}{\frac{1000}{41}+\frac{60452}{1470}}$$

Reduce the fraction \frac{60452}{1470} to lowest terms by extracting and canceling out 14.

$$\frac{1}{26353376}\times \frac{1000}{\frac{1000}{41}+\frac{4318}{105}}$$

Least common multiple of 41 and 105 is 4305. Convert \frac{1000}{41} and \frac{4318}{105} to fractions with denominator 4305.

$$\frac{1}{26353376}\times \frac{1000}{\frac{105000}{4305}+\frac{177038}{4305}}$$

Since \frac{105000}{4305} and \frac{177038}{4305} have the same denominator, add them by adding their numerators.

$$\frac{1}{26353376}\times \frac{1000}{\frac{105000+177038}{4305}}$$

Add 105000 and 177038 to get 282038.

$$\frac{1}{26353376}\times \frac{1000}{\frac{282038}{4305}}$$

Divide 1000 by \frac{282038}{4305} by multiplying 1000 by the reciprocal of \frac{282038}{4305}.

$$\frac{1}{26353376}\times 1000\times \frac{4305}{282038}$$

Express 1000\times \frac{4305}{282038} as a single fraction.

$$\frac{1}{26353376}\times \frac{1000\times 4305}{282038}$$

Multiply 1000 and 4305 to get 4305000.

$$\frac{1}{26353376}\times \frac{4305000}{282038}$$

Reduce the fraction \frac{4305000}{282038} to lowest terms by extracting and canceling out 2.

$$\frac{1}{26353376}\times \frac{2152500}{141019}$$

Multiply \frac{1}{26353376} times \frac{2152500}{141019} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 2152500}{26353376\times 141019}$$

Do the multiplications in the fraction \frac{1\times 2152500}{26353376\times 141019}.

$$\frac{2152500}{3716326730144}$$

Reduce the fraction \frac{2152500}{3716326730144} to lowest terms by extracting and canceling out 28.

$$\frac{76875}{132725954648}$$

Factor

$$\frac{3 \cdot 41 \cdot 5 ^ {4}}{31 \cdot 4549 \cdot 2 ^ {3} \cdot 7 ^ {6}} = 5.792009573702352 \times 10^{-7}$$