Solve 4*1/14^71000/frac{1000{41}+41182/147}

$$\frac{ 4 \cdot 1 }{ { 14 }^{ 7 } } \frac{ 1000 }{ \frac{ 1000 }{ 41 } +41 \frac{ 182 }{ 147 } }$$

Evaluate

$$\frac{15375}{26996680732}\approx 0.00000057$$

Solution Steps

Multiply 4 and 1 to get 4.

$$\frac{4}{14^{7}}\times \frac{1000}{\frac{1000}{41}+\frac{41\times 147+182}{147}}$$

Calculate 14 to the power of 7 and get 105413504.

$$\frac{4}{105413504}\times \frac{1000}{\frac{1000}{41}+\frac{41\times 147+182}{147}}$$

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

$$\frac{1}{26353376}\times \frac{1000}{\frac{1000}{41}+\frac{41\times 147+182}{147}}$$

Multiply 41 and 147 to get 6027.

$$\frac{1}{26353376}\times \frac{1000}{\frac{1000}{41}+\frac{6027+182}{147}}$$

Add 6027 and 182 to get 6209.

$$\frac{1}{26353376}\times \frac{1000}{\frac{1000}{41}+\frac{6209}{147}}$$

Reduce the fraction \frac{6209}{147} to lowest terms by extracting and canceling out 7.

$$\frac{1}{26353376}\times \frac{1000}{\frac{1000}{41}+\frac{887}{21}}$$

Least common multiple of 41 and 21 is 861. Convert \frac{1000}{41} and \frac{887}{21} to fractions with denominator 861.

$$\frac{1}{26353376}\times \frac{1000}{\frac{21000}{861}+\frac{36367}{861}}$$

Since \frac{21000}{861} and \frac{36367}{861} have the same denominator, add them by adding their numerators.

$$\frac{1}{26353376}\times \frac{1000}{\frac{21000+36367}{861}}$$

Add 21000 and 36367 to get 57367.

$$\frac{1}{26353376}\times \frac{1000}{\frac{57367}{861}}$$

Divide 1000 by \frac{57367}{861} by multiplying 1000 by the reciprocal of \frac{57367}{861}.

$$\frac{1}{26353376}\times 1000\times \frac{861}{57367}$$

Express 1000\times \frac{861}{57367} as a single fraction.

$$\frac{1}{26353376}\times \frac{1000\times 861}{57367}$$

Multiply 1000 and 861 to get 861000.

$$\frac{1}{26353376}\times \frac{861000}{57367}$$

Multiply \frac{1}{26353376} times \frac{861000}{57367} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 861000}{26353376\times 57367}$$

Do the multiplications in the fraction \frac{1\times 861000}{26353376\times 57367}.

$$\frac{861000}{1511814120992}$$

Reduce the fraction \frac{861000}{1511814120992} to lowest terms by extracting and canceling out 56.

$$\frac{15375}{26996680732}$$

Factor

$$\frac{3 \cdot 5 ^ {3} \cdot 41}{2 ^ {2} \cdot 7 ^ {6} \cdot 57367} = 5.695144581895039 \times 10^{-7}$$