Solve frac{2^{-1}-(-2)^2+(-3)^-1}{2^2+2^-5}

$$\frac { 2 ^ { - 1 } - ( - 2 ) ^ { 2 } + ( - 3 ) ^ { - 1 } } { 2 ^ { 2 } + 2 ^ { - 5 } }$$

Evaluate

$$-\frac{368}{387}\approx -0.950904393$$

Solution Steps

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

$$\frac{\frac{1}{2}-\left(-2\right)^{2}+\left(-3\right)^{-1}}{2^{2}+2^{-5}}$$

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

$$\frac{\frac{1}{2}-4+\left(-3\right)^{-1}}{2^{2}+2^{-5}}$$

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

$$\frac{-\frac{7}{2}+\left(-3\right)^{-1}}{2^{2}+2^{-5}}$$

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

$$\frac{-\frac{7}{2}-\frac{1}{3}}{2^{2}+2^{-5}}$$

Subtract \frac{1}{3} from -\frac{7}{2} to get -\frac{23}{6}.

$$\frac{-\frac{23}{6}}{2^{2}+2^{-5}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{-\frac{23}{6}}{4+2^{-5}}$$

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

$$\frac{-\frac{23}{6}}{4+\frac{1}{32}}$$

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

$$\frac{-\frac{23}{6}}{\frac{129}{32}}$$

Divide -\frac{23}{6} by \frac{129}{32} by multiplying -\frac{23}{6} by the reciprocal of \frac{129}{32}.

$$-\frac{23}{6}\times \frac{32}{129}$$

Multiply -\frac{23}{6} and \frac{32}{129} to get -\frac{368}{387}.

$$-\frac{368}{387}$$

Factor

$$-\frac{368}{387} = -0.9509043927648578$$