Solve 3(1/2)^3-5(-1/2)^2+5*2^-1-3*2^0

$$3 ( \frac { 1 } { 2 } ) ^ { 3 } - 5 ( \frac { - 1 } { 2 } ) ^ { 2 } + 5 \times 2 ^ { - 1 } - 3 \times 2 ^ { 0 }$$

Evaluate

$$-\frac{11}{8}=-1.375$$

Solution Steps

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

$$3\times \frac{1}{8}-5\times \left(\frac{-1}{2}\right)^{2}+5\times 2^{-1}-3\times 2^{0}$$

Multiply 3 and \frac{1}{8} to get \frac{3}{8}.

$$\frac{3}{8}-5\times \left(\frac{-1}{2}\right)^{2}+5\times 2^{-1}-3\times 2^{0}$$

Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

$$\frac{3}{8}-5\left(-\frac{1}{2}\right)^{2}+5\times 2^{-1}-3\times 2^{0}$$

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

$$\frac{3}{8}-5\times \frac{1}{4}+5\times 2^{-1}-3\times 2^{0}$$

Multiply 5 and \frac{1}{4} to get \frac{5}{4}.

$$\frac{3}{8}-\frac{5}{4}+5\times 2^{-1}-3\times 2^{0}$$

Subtract \frac{5}{4} from \frac{3}{8} to get -\frac{7}{8}.

$$-\frac{7}{8}+5\times 2^{-1}-3\times 2^{0}$$

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

$$-\frac{7}{8}+5\times \frac{1}{2}-3\times 2^{0}$$

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

$$-\frac{7}{8}+\frac{5}{2}-3\times 2^{0}$$

Add -\frac{7}{8} and \frac{5}{2} to get \frac{13}{8}.

$$\frac{13}{8}-3\times 2^{0}$$

Calculate 2 to the power of 0 and get 1.

$$\frac{13}{8}-3\times 1$$

Multiply 3 and 1 to get 3.

$$\frac{13}{8}-3$$

Subtract 3 from \frac{13}{8} to get -\frac{11}{8}.

$$-\frac{11}{8}$$

Factor

$$-\frac{11}{8} = -1\frac{3}{8} = -1.375$$