Solve {left(-3/2right)}^6+{left(-3/2right)}^4-8{left(-3/2right)}^2+4(-3/2)+1

$${ \left(- \frac{ 3 }{ 2 } \right) }^{ 6 } + { \left(- \frac{ 3 }{ 2 } \right) }^{ 4 } -8 { \left(- \frac{ 3 }{ 2 } \right) }^{ 2 } +4(- \frac{ 3 }{ 2 } )+1$$

Evaluate

$$-\frac{419}{64}=-6.546875$$

Solution Steps

Calculate -\frac{3}{2} to the power of 6 and get \frac{729}{64}.

$$\frac{729}{64}+\left(-\frac{3}{2}\right)^{4}-8\left(-\frac{3}{2}\right)^{2}+4\left(-\frac{3}{2}\right)+1$$

Calculate -\frac{3}{2} to the power of 4 and get \frac{81}{16}.

$$\frac{729}{64}+\frac{81}{16}-8\left(-\frac{3}{2}\right)^{2}+4\left(-\frac{3}{2}\right)+1$$

Least common multiple of 64 and 16 is 64. Convert \frac{729}{64} and \frac{81}{16} to fractions with denominator 64.

$$\frac{729}{64}+\frac{324}{64}-8\left(-\frac{3}{2}\right)^{2}+4\left(-\frac{3}{2}\right)+1$$

Since \frac{729}{64} and \frac{324}{64} have the same denominator, add them by adding their numerators.

$$\frac{729+324}{64}-8\left(-\frac{3}{2}\right)^{2}+4\left(-\frac{3}{2}\right)+1$$

Add 729 and 324 to get 1053.

$$\frac{1053}{64}-8\left(-\frac{3}{2}\right)^{2}+4\left(-\frac{3}{2}\right)+1$$

Calculate -\frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$\frac{1053}{64}-8\times \frac{9}{4}+4\left(-\frac{3}{2}\right)+1$$

Express 8\times \frac{9}{4} as a single fraction.

$$\frac{1053}{64}-\frac{8\times 9}{4}+4\left(-\frac{3}{2}\right)+1$$

Multiply 8 and 9 to get 72.

$$\frac{1053}{64}-\frac{72}{4}+4\left(-\frac{3}{2}\right)+1$$

Divide 72 by 4 to get 18.

$$\frac{1053}{64}-18+4\left(-\frac{3}{2}\right)+1$$

Convert 18 to fraction \frac{1152}{64}.

$$\frac{1053}{64}-\frac{1152}{64}+4\left(-\frac{3}{2}\right)+1$$

Since \frac{1053}{64} and \frac{1152}{64} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1053-1152}{64}+4\left(-\frac{3}{2}\right)+1$$

Subtract 1152 from 1053 to get -99.

$$-\frac{99}{64}+4\left(-\frac{3}{2}\right)+1$$

Express 4\left(-\frac{3}{2}\right) as a single fraction.

$$-\frac{99}{64}+\frac{4\left(-3\right)}{2}+1$$

Multiply 4 and -3 to get -12.

$$-\frac{99}{64}+\frac{-12}{2}+1$$

Divide -12 by 2 to get -6.

$$-\frac{99}{64}-6+1$$

Convert 6 to fraction \frac{384}{64}.

$$-\frac{99}{64}-\frac{384}{64}+1$$

Since -\frac{99}{64} and \frac{384}{64} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-99-384}{64}+1$$

Subtract 384 from -99 to get -483.

$$-\frac{483}{64}+1$$

Convert 1 to fraction \frac{64}{64}.

$$-\frac{483}{64}+\frac{64}{64}$$

Since -\frac{483}{64} and \frac{64}{64} have the same denominator, add them by adding their numerators.

$$\frac{-483+64}{64}$$

Add -483 and 64 to get -419.

$$-\frac{419}{64}$$

Factor

$$-\frac{419}{64} = -6\frac{35}{64} = -6.546875$$