Solve 1377^3/3750000-1377^2/1000+1546371(1377)/1250000+1064

$$\frac{ { 1377 }^{ 3 } }{ 3750000 } - \frac{ { 1377 }^{ 2 } }{ 1000 } + \frac{ 1546371(1377) }{ 1250000 } +1064$$

Evaluate

$$\frac{489878707}{312500}=1567.6118624$$

Solution Steps

Calculate 1377 to the power of 3 and get 2610969633.

$$\frac{2610969633}{3750000}-\frac{1377^{2}}{1000}+\frac{1546371\times 1377}{1250000}+1064$$

Reduce the fraction \frac{2610969633}{3750000} to lowest terms by extracting and canceling out 3.

$$\frac{870323211}{1250000}-\frac{1377^{2}}{1000}+\frac{1546371\times 1377}{1250000}+1064$$

Calculate 1377 to the power of 2 and get 1896129.

$$\frac{870323211}{1250000}-\frac{1896129}{1000}+\frac{1546371\times 1377}{1250000}+1064$$

Least common multiple of 1250000 and 1000 is 1250000. Convert \frac{870323211}{1250000} and \frac{1896129}{1000} to fractions with denominator 1250000.

$$\frac{870323211}{1250000}-\frac{2370161250}{1250000}+\frac{1546371\times 1377}{1250000}+1064$$

Since \frac{870323211}{1250000} and \frac{2370161250}{1250000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{870323211-2370161250}{1250000}+\frac{1546371\times 1377}{1250000}+1064$$

Subtract 2370161250 from 870323211 to get -1499838039.

$$-\frac{1499838039}{1250000}+\frac{1546371\times 1377}{1250000}+1064$$

Multiply 1546371 and 1377 to get 2129352867.

$$-\frac{1499838039}{1250000}+\frac{2129352867}{1250000}+1064$$

Since -\frac{1499838039}{1250000} and \frac{2129352867}{1250000} have the same denominator, add them by adding their numerators.

$$\frac{-1499838039+2129352867}{1250000}+1064$$

Add -1499838039 and 2129352867 to get 629514828.

$$\frac{629514828}{1250000}+1064$$

Reduce the fraction \frac{629514828}{1250000} to lowest terms by extracting and canceling out 4.

$$\frac{157378707}{312500}+1064$$

Convert 1064 to fraction \frac{332500000}{312500}.

$$\frac{157378707}{312500}+\frac{332500000}{312500}$$

Since \frac{157378707}{312500} and \frac{332500000}{312500} have the same denominator, add them by adding their numerators.

$$\frac{157378707+332500000}{312500}$$

Add 157378707 and 332500000 to get 489878707.

$$\frac{489878707}{312500}$$

Factor

$$\frac{489878707}{2 ^ {2} \cdot 5 ^ {7}} = 1567\frac{191207}{312500} = 1567.6118624$$