Solve (2/5)^-2-(1/2)^-3-(3/2)^-2

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

Evaluate

$$-\frac{79}{36}\approx -2.194444444$$

Solution Steps

Calculate \frac{2}{5} to the power of -2 and get \frac{25}{4}.

$$\frac{25}{4}-\left(\frac{1}{2}\right)^{-3}-\left(\frac{3}{2}\right)^{-2}$$

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

$$\frac{25}{4}-8-\left(\frac{3}{2}\right)^{-2}$$

Subtract 8 from \frac{25}{4} to get -\frac{7}{4}.

$$-\frac{7}{4}-\left(\frac{3}{2}\right)^{-2}$$

Calculate \frac{3}{2} to the power of -2 and get \frac{4}{9}.

$$-\frac{7}{4}-\frac{4}{9}$$

Subtract \frac{4}{9} from -\frac{7}{4} to get -\frac{79}{36}.

$$-\frac{79}{36}$$

Factor

$$-\frac{79}{36} = -2\frac{7}{36} = -2.1944444444444446$$