Solve frac{2^{-1}-(-2)^2+(-3)^-1}{2^2+2^-6}

$$\frac { 2 ^ { - 1 } - ( - 2 ) ^ { 2 } + ( - 3 ) ^ { - 1 } } { 2 ^ { 2 } + 2 ^ { - 6 } }$$

Evaluate

$$-\frac{736}{771}\approx -0.95460441$$

Solution Steps

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

$$\frac{\frac{1}{2}-\left(-2\right)^{2}+\left(-3\right)^{-1}}{2^{2}+2^{-6}}$$

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

$$\frac{\frac{1}{2}-4+\left(-3\right)^{-1}}{2^{2}+2^{-6}}$$

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

$$\frac{-\frac{7}{2}+\left(-3\right)^{-1}}{2^{2}+2^{-6}}$$

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

$$\frac{-\frac{7}{2}-\frac{1}{3}}{2^{2}+2^{-6}}$$

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

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

Calculate 2 to the power of 2 and get 4.

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

Calculate 2 to the power of -6 and get \frac{1}{64}.

$$\frac{-\frac{23}{6}}{4+\frac{1}{64}}$$

Add 4 and \frac{1}{64} to get \frac{257}{64}.

$$\frac{-\frac{23}{6}}{\frac{257}{64}}$$

Divide -\frac{23}{6} by \frac{257}{64} by multiplying -\frac{23}{6} by the reciprocal of \frac{257}{64}.

$$-\frac{23}{6}\times \frac{64}{257}$$

Multiply -\frac{23}{6} and \frac{64}{257} to get -\frac{736}{771}.

$$-\frac{736}{771}$$

Factor

$$-\frac{736}{771} = -0.9546044098573282$$