Solve (-2+10*{-1/2*2^-1}+1/2^2)^2

$$( - 2 + 10 \cdot \{ \frac { - 1 } { 2 } \cdot 2 ^ { - 1 } \} + \frac { 1 } { 2 ^ { 2 } } ) ^ { 2 }$$

Evaluate

$$\frac{289}{16}=18.0625$$

Solution Steps

Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

$$\left(-2+10\left(-\frac{1}{2}\right)\times 2^{-1}+\frac{1}{2^{2}}\right)^{2}$$

Multiply 10 and -\frac{1}{2} to get -5.

$$\left(-2-5\times 2^{-1}+\frac{1}{2^{2}}\right)^{2}$$

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

$$\left(-2-5\times \frac{1}{2}+\frac{1}{2^{2}}\right)^{2}$$

Multiply -5 and \frac{1}{2} to get -\frac{5}{2}.

$$\left(-2-\frac{5}{2}+\frac{1}{2^{2}}\right)^{2}$$

Subtract \frac{5}{2} from -2 to get -\frac{9}{2}.

$$\left(-\frac{9}{2}+\frac{1}{2^{2}}\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$\left(-\frac{9}{2}+\frac{1}{4}\right)^{2}$$

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

$$\left(-\frac{17}{4}\right)^{2}$$

Calculate -\frac{17}{4} to the power of 2 and get \frac{289}{16}.

$$\frac{289}{16}$$

Factor

$$\frac{17 ^ {2}}{2 ^ {4}} = 18\frac{1}{16} = 18.0625$$