Solve 2^circ-2^-2/2-2(2)^-2

$$\frac { 2 ^ { \circ } - 2 ^ { - 2 } } { 2 - 2 ( 2 ) ^ { - 2 } }$$

Evaluate

$$\frac{7}{6}\approx 1.166666667$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and -2 to get -1.

$$\frac{2-2^{-2}}{2-2^{-1}}$$

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

$$\frac{2-\frac{1}{4}}{2-2^{-1}}$$

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

$$\frac{\frac{7}{4}}{2-2^{-1}}$$

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

$$\frac{\frac{7}{4}}{2-\frac{1}{2}}$$

Subtract \frac{1}{2} from 2 to get \frac{3}{2}.

$$\frac{\frac{7}{4}}{\frac{3}{2}}$$

Divide \frac{7}{4} by \frac{3}{2} by multiplying \frac{7}{4} by the reciprocal of \frac{3}{2}.

$$\frac{7}{4}\times \frac{2}{3}$$

Multiply \frac{7}{4} and \frac{2}{3} to get \frac{7}{6}.

$$\frac{7}{6}$$

Factor

$$\frac{7}{2 \cdot 3} = 1\frac{1}{6} = 1.1666666666666667$$