Solve {l}{2/3(4)^frac{3{2}}-1/2(4)^2}{-2/3+1/2}

$$\left. \begin{array} { l } { \frac { 2 } { 3 } ( 4 ) ^ { \frac { 3 } { 2 } } - \frac { 1 } { 2 } ( 4 ) ^ { 2 } } \\ { - \frac { 2 } { 3 } + \frac { 1 } { 2 } } \end{array} \right.$$

Evaluate

$$-\frac{17}{6}\approx -2.833333333$$

Solution Steps

Calculate 4 to the power of \frac{3}{2} and get 8.

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

Multiply \frac{2}{3} and 8 to get \frac{16}{3}.

$$\frac{16}{3}-\frac{1}{2}\times 4^{2}-\frac{2}{3}+\frac{1}{2}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{16}{3}-\frac{1}{2}\times 16-\frac{2}{3}+\frac{1}{2}$$

Multiply \frac{1}{2} and 16 to get 8.

$$\frac{16}{3}-8-\frac{2}{3}+\frac{1}{2}$$

Subtract 8 from \frac{16}{3} to get -\frac{8}{3}.

$$-\frac{8}{3}-\frac{2}{3}+\frac{1}{2}$$

Subtract \frac{2}{3} from -\frac{8}{3} to get -\frac{10}{3}.

$$-\frac{10}{3}+\frac{1}{2}$$

Add -\frac{10}{3} and \frac{1}{2} to get -\frac{17}{6}.

$$-\frac{17}{6}$$

Factor

$$-\frac{17}{6} = -2\frac{5}{6} = -2.8333333333333335$$