Solve frac{2^{-1}-(-2)^2+(-2)^-1}{2^2+2^-5}

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

Evaluate

$$-\frac{128}{129}\approx -0.992248062$$

Solution Steps

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

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

Calculate -2 to the power of 2 and get 4.

$$\frac{\frac{1}{2}-4+\left(-2\right)^{-1}}{2^{2}+2^{-5}}$$

Subtract 4 from \frac{1}{2} to get -\frac{7}{2}.

$$\frac{-\frac{7}{2}+\left(-2\right)^{-1}}{2^{2}+2^{-5}}$$

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

$$\frac{-\frac{7}{2}-\frac{1}{2}}{2^{2}+2^{-5}}$$

Subtract \frac{1}{2} from -\frac{7}{2} to get -4.

$$\frac{-4}{2^{2}+2^{-5}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{-4}{4+2^{-5}}$$

Calculate 2 to the power of -5 and get \frac{1}{32}.

$$\frac{-4}{4+\frac{1}{32}}$$

Add 4 and \frac{1}{32} to get \frac{129}{32}.

$$\frac{-4}{\frac{129}{32}}$$

Divide -4 by \frac{129}{32} by multiplying -4 by the reciprocal of \frac{129}{32}.

$$-4\times \frac{32}{129}$$

Multiply -4 and \frac{32}{129} to get -\frac{128}{129}.

$$-\frac{128}{129}$$

Factor

$$-\frac{128}{129} = -0.9922480620155039$$