Solve 2^0-3^-2/2-2(2)^-2

$$\frac { 2 ^ { 0 } - 3 ^ { - 2 } } { 2 - 2 ( 2 ) ^ { - 2 } }$$

Evaluate

$$\frac{16}{27}\approx 0.592592593$$

Solution Steps

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

$$\frac{2^{0}-3^{-2}}{2-2^{-1}}$$

Calculate 2 to the power of 0 and get 1.

$$\frac{1-3^{-2}}{2-2^{-1}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{1-\frac{1}{9}}{2-2^{-1}}$$

Subtract \frac{1}{9} from 1 to get \frac{8}{9}.

$$\frac{\frac{8}{9}}{2-2^{-1}}$$

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

$$\frac{\frac{8}{9}}{2-\frac{1}{2}}$$

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

$$\frac{\frac{8}{9}}{\frac{3}{2}}$$

Divide \frac{8}{9} by \frac{3}{2} by multiplying \frac{8}{9} by the reciprocal of \frac{3}{2}.

$$\frac{8}{9}\times \frac{2}{3}$$

Multiply \frac{8}{9} and \frac{2}{3} to get \frac{16}{27}.

$$\frac{16}{27}$$

Factor

$$\frac{2 ^ {4}}{3 ^ {3}} = 0.5925925925925926$$