Solve -[1/2((-1)^4/4+1^3-4)]

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

Evaluate

$$\frac{11}{8}=1.375$$

Solution Steps

Calculate -1 to the power of 4 and get 1.

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

Calculate 1 to the power of 3 and get 1.

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

Convert 1 to fraction \frac{4}{4}.

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

Since \frac{1}{4} and \frac{4}{4} have the same denominator, add them by adding their numerators.

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

Add 1 and 4 to get 5.

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

Convert 4 to fraction \frac{16}{4}.

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

Since \frac{5}{4} and \frac{16}{4} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{2}\times \frac{5-16}{4}$$

Subtract 16 from 5 to get -11.

$$-\frac{1}{2}\left(-\frac{11}{4}\right)$$

Multiply \frac{1}{2} times -\frac{11}{4} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{1\left(-11\right)}{2\times 4}$$

Do the multiplications in the fraction \frac{1\left(-11\right)}{2\times 4}.

$$-\frac{-11}{8}$$

Fraction \frac{-11}{8} can be rewritten as -\frac{11}{8} by extracting the negative sign.

$$-\left(-\frac{11}{8}\right)$$

The opposite of -\frac{11}{8} is \frac{11}{8}.

$$\frac{11}{8}$$

Factor

$$\frac{11}{2 ^ {3}} = 1\frac{3}{8} = 1.375$$