Solve 1/2+1/2-(1-1/2)^3:(2/4)^2-(frac{1}{2})^1

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

Evaluate

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Solution Steps

Add \frac{1}{2} and \frac{1}{2} to get 1.

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

Subtract \frac{1}{2} from 1 to get \frac{1}{2}.

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

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

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

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

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

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

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

Divide \frac{1}{8} by \frac{1}{4} by multiplying \frac{1}{8} by the reciprocal of \frac{1}{4}.

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

Multiply \frac{1}{8} and 4 to get \frac{1}{2}.

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

Subtract \frac{1}{2} from 1 to get \frac{1}{2}.

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

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

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

Subtract \frac{1}{2} from \frac{1}{2} to get 0.

$$0$$

Factor

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