Solve (-1/2)^4+(3/2)^3-(-1/4)^2+(5/1)

$$( \frac { - 1 } { 2 } ) ^ { 4 } + ( \frac { 3 } { 2 } ) ^ { 3 } - ( \frac { - 1 } { 4 } ) ^ { 2 } + ( \frac { 5 } { 1 } )$$

Evaluate

$$\frac{67}{8}=8.375$$

Solution Steps

Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

$$\left(-\frac{1}{2}\right)^{4}+\left(\frac{3}{2}\right)^{3}-\left(\frac{-1}{4}\right)^{2}+\frac{5}{1}$$

Calculate -\frac{1}{2} to the power of 4 and get \frac{1}{16}.

$$\frac{1}{16}+\left(\frac{3}{2}\right)^{3}-\left(\frac{-1}{4}\right)^{2}+\frac{5}{1}$$

Calculate \frac{3}{2} to the power of 3 and get \frac{27}{8}.

$$\frac{1}{16}+\frac{27}{8}-\left(\frac{-1}{4}\right)^{2}+\frac{5}{1}$$

Add \frac{1}{16} and \frac{27}{8} to get \frac{55}{16}.

$$\frac{55}{16}-\left(\frac{-1}{4}\right)^{2}+\frac{5}{1}$$

Fraction \frac{-1}{4} can be rewritten as -\frac{1}{4} by extracting the negative sign.

$$\frac{55}{16}-\left(-\frac{1}{4}\right)^{2}+\frac{5}{1}$$

Calculate -\frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$\frac{55}{16}-\frac{1}{16}+\frac{5}{1}$$

Subtract \frac{1}{16} from \frac{55}{16} to get \frac{27}{8}.

$$\frac{27}{8}+\frac{5}{1}$$

Anything divided by one gives itself.

$$\frac{27}{8}+5$$

Add \frac{27}{8} and 5 to get \frac{67}{8}.

$$\frac{67}{8}$$

Factor

$$\frac{67}{2 ^ {3}} = 8\frac{3}{8} = 8.375$$