Solve (1/2)^-2+[2^-1-(-2)^-1]^-1

$$( \frac { 1 } { 2 } ) ^ { - 2 } + [ 2 ^ { - 1 } - ( - 2 ) ^ { - 1 } ] ^ { - 1 }$$

Evaluate

$$5$$

Solution Steps

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

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

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

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

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

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

The opposite of -\frac{1}{2} is \frac{1}{2}.

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

Add \frac{1}{2} and \frac{1}{2} to get 1.

$$4+1^{-1}$$

Calculate 1 to the power of -1 and get 1.

$$4+1$$

Add 4 and 1 to get 5.

$$5$$

Factor

$$5$$