Solve 1-(1/3)^3:(1/2-1)^2

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

Evaluate

$$\frac{23}{27}\approx 0.851851852$$

Solution Steps

Calculate \frac{1}{3} to the power of 3 and get \frac{1}{27}.

$$1-\frac{\frac{1}{27}}{\left(\frac{1}{2}-1\right)^{2}}$$

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

$$1-\frac{\frac{1}{27}}{\left(-\frac{1}{2}\right)^{2}}$$

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

$$1-\frac{\frac{1}{27}}{\frac{1}{4}}$$

Divide \frac{1}{27} by \frac{1}{4} by multiplying \frac{1}{27} by the reciprocal of \frac{1}{4}.

$$1-\frac{1}{27}\times 4$$

Multiply \frac{1}{27} and 4 to get \frac{4}{27}.

$$1-\frac{4}{27}$$

Subtract \frac{4}{27} from 1 to get \frac{23}{27}.

$$\frac{23}{27}$$

Factor

$$\frac{23}{3 ^ {3}} = 0.8518518518518519$$