Solve (-1/2)^{2}+4[(-1/4)^-2(1/4)^7]+(-1/2)^2-(-frac{1}{2})^2

$$( - \frac { 1 } { 2 } ) ^ { 2 } + 4 [ ( - \frac { 1 } { 4 } ) ^ { - 2 } ( \frac { 1 } { 4 } ) ^ { 7 } ] + ( - \frac { 1 } { 2 } ) ^ { 2 } - ( - \frac { 1 } { 2 } ) ^ { 2 }$$

Evaluate

$$\frac{65}{256}=0.25390625$$

Solution Steps

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

$$\frac{1}{4}+4\left(-\frac{1}{4}\right)^{-2}\times \left(\frac{1}{4}\right)^{7}+\left(-\frac{1}{2}\right)^{2}-\left(-\frac{1}{2}\right)^{2}$$

Calculate -\frac{1}{4} to the power of -2 and get 16.

$$\frac{1}{4}+4\times 16\times \left(\frac{1}{4}\right)^{7}+\left(-\frac{1}{2}\right)^{2}-\left(-\frac{1}{2}\right)^{2}$$

Multiply 4 and 16 to get 64.

$$\frac{1}{4}+64\times \left(\frac{1}{4}\right)^{7}+\left(-\frac{1}{2}\right)^{2}-\left(-\frac{1}{2}\right)^{2}$$

Calculate \frac{1}{4} to the power of 7 and get \frac{1}{16384}.

$$\frac{1}{4}+64\times \frac{1}{16384}+\left(-\frac{1}{2}\right)^{2}-\left(-\frac{1}{2}\right)^{2}$$

Multiply 64 and \frac{1}{16384} to get \frac{1}{256}.

$$\frac{1}{4}+\frac{1}{256}+\left(-\frac{1}{2}\right)^{2}-\left(-\frac{1}{2}\right)^{2}$$

Add \frac{1}{4} and \frac{1}{256} to get \frac{65}{256}.

$$\frac{65}{256}+\left(-\frac{1}{2}\right)^{2}-\left(-\frac{1}{2}\right)^{2}$$

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

$$\frac{65}{256}+\frac{1}{4}-\left(-\frac{1}{2}\right)^{2}$$

Add \frac{65}{256} and \frac{1}{4} to get \frac{129}{256}.

$$\frac{129}{256}-\left(-\frac{1}{2}\right)^{2}$$

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

$$\frac{129}{256}-\frac{1}{4}$$

Subtract \frac{1}{4} from \frac{129}{256} to get \frac{65}{256}.

$$\frac{65}{256}$$

Factor

$$\frac{5 \cdot 13}{2 ^ {8}} = 0.25390625$$