Solve (-1/2)^3-[(1/2)^2div(-1)-1/16]*(-2)div(-1)^2012

$$( - \frac { 1 } { 2 } ) ^ { 3 } - [ ( \frac { 1 } { 2 } ) ^ { 2 } \div ( - 1 ) - \frac { 1 } { 16 } ] \times ( - 2 ) \div ( - 1 ) ^ { 2012 }$$

Evaluate

$$-\frac{3}{4}=-0.75$$

Solution Steps

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

$$-\frac{1}{8}-\frac{\left(\frac{\left(\frac{1}{2}\right)^{2}}{-1}-\frac{1}{16}\right)\left(-2\right)}{\left(-1\right)^{2012}}$$

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

$$-\frac{1}{8}-\frac{\left(\frac{\frac{1}{4}}{-1}-\frac{1}{16}\right)\left(-2\right)}{\left(-1\right)^{2012}}$$

Express \frac{\frac{1}{4}}{-1} as a single fraction.

$$-\frac{1}{8}-\frac{\left(\frac{1}{4\left(-1\right)}-\frac{1}{16}\right)\left(-2\right)}{\left(-1\right)^{2012}}$$

Multiply 4 and -1 to get -4.

$$-\frac{1}{8}-\frac{\left(\frac{1}{-4}-\frac{1}{16}\right)\left(-2\right)}{\left(-1\right)^{2012}}$$

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

$$-\frac{1}{8}-\frac{\left(-\frac{1}{4}-\frac{1}{16}\right)\left(-2\right)}{\left(-1\right)^{2012}}$$

Least common multiple of 4 and 16 is 16. Convert -\frac{1}{4} and \frac{1}{16} to fractions with denominator 16.

$$-\frac{1}{8}-\frac{\left(-\frac{4}{16}-\frac{1}{16}\right)\left(-2\right)}{\left(-1\right)^{2012}}$$

Since -\frac{4}{16} and \frac{1}{16} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{8}-\frac{\frac{-4-1}{16}\left(-2\right)}{\left(-1\right)^{2012}}$$

Subtract 1 from -4 to get -5.

$$-\frac{1}{8}-\frac{-\frac{5}{16}\left(-2\right)}{\left(-1\right)^{2012}}$$

Express -\frac{5}{16}\left(-2\right) as a single fraction.

$$-\frac{1}{8}-\frac{\frac{-5\left(-2\right)}{16}}{\left(-1\right)^{2012}}$$

Multiply -5 and -2 to get 10.

$$-\frac{1}{8}-\frac{\frac{10}{16}}{\left(-1\right)^{2012}}$$

Reduce the fraction \frac{10}{16} to lowest terms by extracting and canceling out 2.

$$-\frac{1}{8}-\frac{\frac{5}{8}}{\left(-1\right)^{2012}}$$

Calculate -1 to the power of 2012 and get 1.

$$-\frac{1}{8}-\frac{\frac{5}{8}}{1}$$

Anything divided by one gives itself.

$$-\frac{1}{8}-\frac{5}{8}$$

Since -\frac{1}{8} and \frac{5}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-1-5}{8}$$

Subtract 5 from -1 to get -6.

$$\frac{-6}{8}$$

Reduce the fraction \frac{-6}{8} to lowest terms by extracting and canceling out 2.

$$-\frac{3}{4}$$

Factor

$$-\frac{3}{4} = -0.75$$