Solve 2(1/2)^4-(1/2)^3-6(1/2)^2+5(1/2)-4

$$2 ( \frac { 1 } { 2 } ) ^ { 4 } - ( \frac { 1 } { 2 } ) ^ { 3 } - 6 ( \frac { 1 } { 2 } ) ^ { 2 } + 5 ( \frac { 1 } { 2 } ) - 4$$

Evaluate

$$-3$$

Solution Steps

Calculate \frac{1}{2} to the power of 4 and get \frac{1}{16}.

$$2\times \frac{1}{16}-\left(\frac{1}{2}\right)^{3}-6\times \left(\frac{1}{2}\right)^{2}+5\times \frac{1}{2}-4$$

Multiply 2 and \frac{1}{16} to get \frac{2}{16}.

$$\frac{2}{16}-\left(\frac{1}{2}\right)^{3}-6\times \left(\frac{1}{2}\right)^{2}+5\times \frac{1}{2}-4$$

Reduce the fraction \frac{2}{16} to lowest terms by extracting and canceling out 2.

$$\frac{1}{8}-\left(\frac{1}{2}\right)^{3}-6\times \left(\frac{1}{2}\right)^{2}+5\times \frac{1}{2}-4$$

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

$$\frac{1}{8}-\frac{1}{8}-6\times \left(\frac{1}{2}\right)^{2}+5\times \frac{1}{2}-4$$

Subtract \frac{1}{8} from \frac{1}{8} to get 0.

$$0-6\times \left(\frac{1}{2}\right)^{2}+5\times \frac{1}{2}-4$$

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

$$0-6\times \frac{1}{4}+5\times \frac{1}{2}-4$$

Multiply 6 and \frac{1}{4} to get \frac{6}{4}.

$$0-\frac{6}{4}+5\times \frac{1}{2}-4$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$0-\frac{3}{2}+5\times \frac{1}{2}-4$$

Subtract \frac{3}{2} from 0 to get -\frac{3}{2}.

$$-\frac{3}{2}+5\times \frac{1}{2}-4$$

Multiply 5 and \frac{1}{2} to get \frac{5}{2}.

$$-\frac{3}{2}+\frac{5}{2}-4$$

Since -\frac{3}{2} and \frac{5}{2} have the same denominator, add them by adding their numerators.

$$\frac{-3+5}{2}-4$$

Add -3 and 5 to get 2.

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

Divide 2 by 2 to get 1.

$$1-4$$

Subtract 4 from 1 to get -3.

$$-3$$

Factor

$$-3$$