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

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

Evaluate

$$\frac{65}{96}\approx 0.677083333$$

Solution Steps

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

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

Calculate -2 to the power of 3 and get -8.

$$\frac{\frac{1}{4}-\left(-8\right)+\left(-2\right)^{-3}}{2^{2}+2^{3}}$$

The opposite of -8 is 8.

$$\frac{\frac{1}{4}+8+\left(-2\right)^{-3}}{2^{2}+2^{3}}$$

Add \frac{1}{4} and 8 to get \frac{33}{4}.

$$\frac{\frac{33}{4}+\left(-2\right)^{-3}}{2^{2}+2^{3}}$$

Calculate -2 to the power of -3 and get -\frac{1}{8}.

$$\frac{\frac{33}{4}-\frac{1}{8}}{2^{2}+2^{3}}$$

Subtract \frac{1}{8} from \frac{33}{4} to get \frac{65}{8}.

$$\frac{\frac{65}{8}}{2^{2}+2^{3}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{\frac{65}{8}}{4+2^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{\frac{65}{8}}{4+8}$$

Add 4 and 8 to get 12.

$$\frac{\frac{65}{8}}{12}$$

Express \frac{\frac{65}{8}}{12} as a single fraction.

$$\frac{65}{8\times 12}$$

Multiply 8 and 12 to get 96.

$$\frac{65}{96}$$

Factor

$$\frac{5 \cdot 13}{2 ^ {5} \cdot 3} = 0.6770833333333334$$