Solve 2^-2+1/2*(-1+3-1/2)^-2

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

Evaluate

$$\frac{17}{36}\approx 0.472222222$$

Solution Steps

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

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

Add -1 and 3 to get 2.

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

Subtract \frac{1}{2} from 2 to get \frac{3}{2}.

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

Calculate \frac{3}{2} to the power of -2 and get \frac{4}{9}.

$$\frac{1}{4}+\frac{1}{2}\times \frac{4}{9}$$

Multiply \frac{1}{2} and \frac{4}{9} to get \frac{2}{9}.

$$\frac{1}{4}+\frac{2}{9}$$

Add \frac{1}{4} and \frac{2}{9} to get \frac{17}{36}.

$$\frac{17}{36}$$

Factor

$$\frac{17}{2 ^ {2} \cdot 3 ^ {2}} = 0.4722222222222222$$