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

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

Evaluate

$$\frac{97}{36}\approx 2.694444444$$

Solution Steps

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

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

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

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

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

$$\frac{25}{4}-8\times \frac{4}{9}$$

Multiply 8 and \frac{4}{9} to get \frac{32}{9}.

$$\frac{25}{4}-\frac{32}{9}$$

Subtract \frac{32}{9} from \frac{25}{4} to get \frac{97}{36}.

$$\frac{97}{36}$$

Factor

$$\frac{97}{2 ^ {2} \cdot 3 ^ {2}} = 2\frac{25}{36} = 2.6944444444444446$$