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

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

Evaluate

$$-\frac{47}{144}\approx -0.326388889$$

Solution Steps

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

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

Calculate -\frac{2}{3} to the power of 3 and get -\frac{8}{27}.

$$\frac{1}{2}+3\left(-\frac{8}{27}\right)+4^{-2}$$

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

$$\frac{1}{2}-\frac{8}{9}+4^{-2}$$

Subtract \frac{8}{9} from \frac{1}{2} to get -\frac{7}{18}.

$$-\frac{7}{18}+4^{-2}$$

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

$$-\frac{7}{18}+\frac{1}{16}$$

Add -\frac{7}{18} and \frac{1}{16} to get -\frac{47}{144}.

$$-\frac{47}{144}$$

Factor

$$-\frac{47}{144} = -0.3263888888888889$$