Solve 103(1(1750/6400)+1{left(1750/6400right)}^2+1{left(1750/6400right)}^3)=

$$103(1( \frac{ 1750 }{ 6400 } )+1 { \left( \frac{ 1750 }{ 6400 } \right) }^{ 2 } +1 { \left( \frac{ 1750 }{ 6400 } \right) }^{ 3 } )=$$

Evaluate

$$\frac{79630845}{2097152}\approx 37.970945835$$

Solution Steps

Reduce the fraction \frac{1750}{6400} to lowest terms by extracting and canceling out 50.

$$103\left(1\times \frac{35}{128}+1\times \left(\frac{1750}{6400}\right)^{2}+1\times \left(\frac{1750}{6400}\right)^{3}\right)$$

Multiply 1 and \frac{35}{128} to get \frac{35}{128}.

$$103\left(\frac{35}{128}+1\times \left(\frac{1750}{6400}\right)^{2}+1\times \left(\frac{1750}{6400}\right)^{3}\right)$$

Reduce the fraction \frac{1750}{6400} to lowest terms by extracting and canceling out 50.

$$103\left(\frac{35}{128}+1\times \left(\frac{35}{128}\right)^{2}+1\times \left(\frac{1750}{6400}\right)^{3}\right)$$

Calculate \frac{35}{128} to the power of 2 and get \frac{1225}{16384}.

$$103\left(\frac{35}{128}+1\times \frac{1225}{16384}+1\times \left(\frac{1750}{6400}\right)^{3}\right)$$

Multiply 1 and \frac{1225}{16384} to get \frac{1225}{16384}.

$$103\left(\frac{35}{128}+\frac{1225}{16384}+1\times \left(\frac{1750}{6400}\right)^{3}\right)$$

Add \frac{35}{128} and \frac{1225}{16384} to get \frac{5705}{16384}.

$$103\left(\frac{5705}{16384}+1\times \left(\frac{1750}{6400}\right)^{3}\right)$$

Reduce the fraction \frac{1750}{6400} to lowest terms by extracting and canceling out 50.

$$103\left(\frac{5705}{16384}+1\times \left(\frac{35}{128}\right)^{3}\right)$$

Calculate \frac{35}{128} to the power of 3 and get \frac{42875}{2097152}.

$$103\left(\frac{5705}{16384}+1\times \frac{42875}{2097152}\right)$$

Multiply 1 and \frac{42875}{2097152} to get \frac{42875}{2097152}.

$$103\left(\frac{5705}{16384}+\frac{42875}{2097152}\right)$$

Add \frac{5705}{16384} and \frac{42875}{2097152} to get \frac{773115}{2097152}.

$$103\times \frac{773115}{2097152}$$

Multiply 103 and \frac{773115}{2097152} to get \frac{79630845}{2097152}.

$$\frac{79630845}{2097152}$$

Factor

$$\frac{3 \cdot 5 \cdot 7 \cdot 37 \cdot 103 \cdot 199}{2 ^ {21}} = 37\frac{2036221}{2097152} = 37.970945835113525$$