Solve -0.25^2/1/{left(-frac{1{2}right)}^3}+left(1/8-1/2right)-1^100

$$\frac{ \frac{ - { 0.25 }^{ 2 } }{ 1 } }{ { \left(- \frac{ 1 }{ 2 } \right) }^{ 3 } } + \left( \frac{ 1 }{ 8 } - \frac{ 1 }{ 2 } \right) { -1 }^{ 100 }$$

Evaluate

$$0.125$$

Solution Steps

Calculate 0.25 to the power of 2 and get 0.0625.

$$\frac{\frac{-0.0625}{1}}{\left(-\frac{1}{2}\right)^{3}}+\left(\frac{1}{8}-\frac{1}{2}\right)\left(-1\right)^{100}$$

Anything divided by one gives itself.

$$\frac{-0.0625}{\left(-\frac{1}{2}\right)^{3}}+\left(\frac{1}{8}-\frac{1}{2}\right)\left(-1\right)^{100}$$

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

$$\frac{-0.0625}{-\frac{1}{8}}+\left(\frac{1}{8}-\frac{1}{2}\right)\left(-1\right)^{100}$$

Divide -0.0625 by -\frac{1}{8} by multiplying -0.0625 by the reciprocal of -\frac{1}{8}.

$$-0.0625\left(-8\right)+\left(\frac{1}{8}-\frac{1}{2}\right)\left(-1\right)^{100}$$

Multiply -0.0625 and -8 to get 0.5.

$$0.5+\left(\frac{1}{8}-\frac{1}{2}\right)\left(-1\right)^{100}$$

Least common multiple of 8 and 2 is 8. Convert \frac{1}{8} and \frac{1}{2} to fractions with denominator 8.

$$0.5+\left(\frac{1}{8}-\frac{4}{8}\right)\left(-1\right)^{100}$$

Since \frac{1}{8} and \frac{4}{8} have the same denominator, subtract them by subtracting their numerators.

$$0.5+\frac{1-4}{8}\left(-1\right)^{100}$$

Subtract 4 from 1 to get -3.

$$0.5-\frac{3}{8}\left(-1\right)^{100}$$

Calculate -1 to the power of 100 and get 1.

$$0.5-\frac{3}{8}$$

Convert decimal number 0.5 to fraction \frac{5}{10}. Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{1}{2}-\frac{3}{8}$$

Least common multiple of 2 and 8 is 8. Convert \frac{1}{2} and \frac{3}{8} to fractions with denominator 8.

$$\frac{4}{8}-\frac{3}{8}$$

Since \frac{4}{8} and \frac{3}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4-3}{8}$$

Subtract 3 from 4 to get 1.

$$\frac{1}{8}$$

Factor

$$\frac{1}{2 ^ {3}} = 0.125$$