Solve 2^-1+|-3|*2^0-sqrt{1/4}

$$2 ^ { - 1 } + | - 3 | \times 2 ^ { 0 } - \sqrt { \frac { 1 } { 4 } }$$

Evaluate

$$3$$

Solution Steps

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

$$\frac{1}{2}+|-3|\times 2^{0}-\sqrt{\frac{1}{4}}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -3 is 3.

$$\frac{1}{2}+3\times 2^{0}-\sqrt{\frac{1}{4}}$$

Calculate 2 to the power of 0 and get 1.

$$\frac{1}{2}+3\times 1-\sqrt{\frac{1}{4}}$$

Multiply 3 and 1 to get 3.

$$\frac{1}{2}+3-\sqrt{\frac{1}{4}}$$

Add \frac{1}{2} and 3 to get \frac{7}{2}.

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

Rewrite the square root of the division \frac{1}{4} as the division of square roots \frac{\sqrt{1}}{\sqrt{4}}. Take the square root of both numerator and denominator.

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

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

$$3$$

Factor

$$3$$