Solve 103(1.36(1750/6400)+0.28{left(1750/6400right)}^2-0.64{left(1750/6400right)}^3)=

$$103(1.36( \frac{ 1750 }{ 6400 } )+0.28 { \left( \frac{ 1750 }{ 6400 } \right) }^{ 2 } -0.64 { \left( \frac{ 1750 }{ 6400 } \right) }^{ 3 } )=$$

Evaluate

$$39.11174163818359375$$

Solution Steps

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

$$103\left(1.36\times \frac{35}{128}+0.28\times \left(\frac{1750}{6400}\right)^{2}-0.64\times \left(\frac{1750}{6400}\right)^{3}\right)$$

Multiply 1.36 and \frac{35}{128} to get \frac{119}{320}.

$$103\left(\frac{119}{320}+0.28\times \left(\frac{1750}{6400}\right)^{2}-0.64\times \left(\frac{1750}{6400}\right)^{3}\right)$$

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

$$103\left(\frac{119}{320}+0.28\times \left(\frac{35}{128}\right)^{2}-0.64\times \left(\frac{1750}{6400}\right)^{3}\right)$$

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

$$103\left(\frac{119}{320}+0.28\times \frac{1225}{16384}-0.64\times \left(\frac{1750}{6400}\right)^{3}\right)$$

Multiply 0.28 and \frac{1225}{16384} to get \frac{343}{16384}.

$$103\left(\frac{119}{320}+\frac{343}{16384}-0.64\times \left(\frac{1750}{6400}\right)^{3}\right)$$

Add \frac{119}{320} and \frac{343}{16384} to get \frac{32179}{81920}.

$$103\left(\frac{32179}{81920}-0.64\times \left(\frac{1750}{6400}\right)^{3}\right)$$

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

$$103\left(\frac{32179}{81920}-0.64\times \left(\frac{35}{128}\right)^{3}\right)$$

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

$$103\left(\frac{32179}{81920}-0.64\times \frac{42875}{2097152}\right)$$

Multiply 0.64 and \frac{42875}{2097152} to get \frac{1715}{131072}.

$$103\left(\frac{32179}{81920}-\frac{1715}{131072}\right)$$

Subtract \frac{1715}{131072} from \frac{32179}{81920} to get \frac{248857}{655360}.

$$103\times \frac{248857}{655360}$$

Multiply 103 and \frac{248857}{655360} to get \frac{25632271}{655360}.

$$\frac{25632271}{655360}$$

Factor

$$\frac{7 \cdot 73 \cdot 103 \cdot 487}{5 \cdot 2 ^ {17}} = 39\frac{73231}{655360} = 39.111741638183595$$