Solve -1^4-(2-0.5)*1/3*[(-1/2)^2-(1/2)^3]

$$- 1 ^ { 4 } - ( 2 - 0.5 ) \times \frac { 1 } { 3 } \times [ ( - \frac { 1 } { 2 } ) ^ { 2 } - ( \frac { 1 } { 2 } ) ^ { 3 } ]$$

Evaluate

$$-1.0625$$

Solution Steps

Calculate 1 to the power of 4 and get 1.

$$-1-\left(2-0.5\right)\times \frac{1}{3}\left(\left(-\frac{1}{2}\right)^{2}-\left(\frac{1}{2}\right)^{3}\right)$$

Subtract 0.5 from 2 to get 1.5.

$$-1-1.5\times \frac{1}{3}\left(\left(-\frac{1}{2}\right)^{2}-\left(\frac{1}{2}\right)^{3}\right)$$

Convert decimal number 1.5 to fraction \frac{15}{10}. Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.

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

Multiply \frac{3}{2} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 3 in both numerator and denominator.

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

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

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

Calculate \frac{1}{2} to the power of 3 and get \frac{1}{8}.

$$-1-\frac{1}{2}\left(\frac{1}{4}-\frac{1}{8}\right)$$

Least common multiple of 4 and 8 is 8. Convert \frac{1}{4} and \frac{1}{8} to fractions with denominator 8.

$$-1-\frac{1}{2}\left(\frac{2}{8}-\frac{1}{8}\right)$$

Since \frac{2}{8} and \frac{1}{8} have the same denominator, subtract them by subtracting their numerators.

$$-1-\frac{1}{2}\times \frac{2-1}{8}$$

Subtract 1 from 2 to get 1.

$$-1-\frac{1}{2}\times \frac{1}{8}$$

Multiply \frac{1}{2} times \frac{1}{8} by multiplying numerator times numerator and denominator times denominator.

$$-1-\frac{1\times 1}{2\times 8}$$

Do the multiplications in the fraction \frac{1\times 1}{2\times 8}.

$$-1-\frac{1}{16}$$

Convert -1 to fraction -\frac{16}{16}.

$$-\frac{16}{16}-\frac{1}{16}$$

Since -\frac{16}{16} and \frac{1}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-16-1}{16}$$

Subtract 1 from -16 to get -17.

$$-\frac{17}{16}$$

Factor

$$-1.0625$$