Solve {left(13/8right)}^4-3{left(13/8right)}^2+13/4-3

$${ \left( \frac{ 13 }{ 8 } \right) }^{ 4 } -3 { \left( \frac{ 13 }{ 8 } \right) }^{ 2 } + \frac{ 13 }{ 4 } -3$$

Evaluate

$$-\frac{2863}{4096}\approx -0.698974609$$

Solution Steps

Calculate \frac{13}{8} to the power of 4 and get \frac{28561}{4096}.

$$\frac{28561}{4096}-3\times \left(\frac{13}{8}\right)^{2}+\frac{13}{4}-3$$

Calculate \frac{13}{8} to the power of 2 and get \frac{169}{64}.

$$\frac{28561}{4096}-3\times \frac{169}{64}+\frac{13}{4}-3$$

Express 3\times \frac{169}{64} as a single fraction.

$$\frac{28561}{4096}-\frac{3\times 169}{64}+\frac{13}{4}-3$$

Multiply 3 and 169 to get 507.

$$\frac{28561}{4096}-\frac{507}{64}+\frac{13}{4}-3$$

Least common multiple of 4096 and 64 is 4096. Convert \frac{28561}{4096} and \frac{507}{64} to fractions with denominator 4096.

$$\frac{28561}{4096}-\frac{32448}{4096}+\frac{13}{4}-3$$

Since \frac{28561}{4096} and \frac{32448}{4096} have the same denominator, subtract them by subtracting their numerators.

$$\frac{28561-32448}{4096}+\frac{13}{4}-3$$

Subtract 32448 from 28561 to get -3887.

$$-\frac{3887}{4096}+\frac{13}{4}-3$$

Least common multiple of 4096 and 4 is 4096. Convert -\frac{3887}{4096} and \frac{13}{4} to fractions with denominator 4096.

$$-\frac{3887}{4096}+\frac{13312}{4096}-3$$

Since -\frac{3887}{4096} and \frac{13312}{4096} have the same denominator, add them by adding their numerators.

$$\frac{-3887+13312}{4096}-3$$

Add -3887 and 13312 to get 9425.

$$\frac{9425}{4096}-3$$

Convert 3 to fraction \frac{12288}{4096}.

$$\frac{9425}{4096}-\frac{12288}{4096}$$

Since \frac{9425}{4096} and \frac{12288}{4096} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9425-12288}{4096}$$

Subtract 12288 from 9425 to get -2863.

$$-\frac{2863}{4096}$$

Factor

$$-\frac{2863}{4096} = -0.698974609375$$