Solve 103(1(2625/6400)+1{left(2625/6400right)}^2-1{left(2625/6400right)}^3)=

$$103(1( \frac{ 2625 }{ 6400 } )+1 { \left( \frac{ 2625 }{ 6400 } \right) }^{ 2 } -1 { \left( \frac{ 2625 }{ 6400 } \right) }^{ 3 } )=$$

Evaluate

$$\frac{880243665}{16777216}\approx 52.466610968$$

Solution Steps

Reduce the fraction \frac{2625}{6400} to lowest terms by extracting and canceling out 25.

$$103\left(1\times \frac{105}{256}+1\times \left(\frac{2625}{6400}\right)^{2}-1\times \left(\frac{2625}{6400}\right)^{3}\right)$$

Multiply 1 and \frac{105}{256} to get \frac{105}{256}.

$$103\left(\frac{105}{256}+1\times \left(\frac{2625}{6400}\right)^{2}-1\times \left(\frac{2625}{6400}\right)^{3}\right)$$

Reduce the fraction \frac{2625}{6400} to lowest terms by extracting and canceling out 25.

$$103\left(\frac{105}{256}+1\times \left(\frac{105}{256}\right)^{2}-1\times \left(\frac{2625}{6400}\right)^{3}\right)$$

Calculate \frac{105}{256} to the power of 2 and get \frac{11025}{65536}.

$$103\left(\frac{105}{256}+1\times \frac{11025}{65536}-1\times \left(\frac{2625}{6400}\right)^{3}\right)$$

Multiply 1 and \frac{11025}{65536} to get \frac{11025}{65536}.

$$103\left(\frac{105}{256}+\frac{11025}{65536}-1\times \left(\frac{2625}{6400}\right)^{3}\right)$$

Add \frac{105}{256} and \frac{11025}{65536} to get \frac{37905}{65536}.

$$103\left(\frac{37905}{65536}-1\times \left(\frac{2625}{6400}\right)^{3}\right)$$

Reduce the fraction \frac{2625}{6400} to lowest terms by extracting and canceling out 25.

$$103\left(\frac{37905}{65536}-1\times \left(\frac{105}{256}\right)^{3}\right)$$

Calculate \frac{105}{256} to the power of 3 and get \frac{1157625}{16777216}.

$$103\left(\frac{37905}{65536}-1\times \frac{1157625}{16777216}\right)$$

Multiply 1 and \frac{1157625}{16777216} to get \frac{1157625}{16777216}.

$$103\left(\frac{37905}{65536}-\frac{1157625}{16777216}\right)$$

Subtract \frac{1157625}{16777216} from \frac{37905}{65536} to get \frac{8546055}{16777216}.

$$103\times \frac{8546055}{16777216}$$

Multiply 103 and \frac{8546055}{16777216} to get \frac{880243665}{16777216}.

$$\frac{880243665}{16777216}$$

Factor

$$\frac{3 \cdot 5 \cdot 7 \cdot 103 \cdot 199 \cdot 409}{2 ^ {24}} = 52\frac{7828433}{16777216} = 52.466610968112946$$