Solve -{left(2/5right)}^-2-{left(1/2right)}^-3-{left(3/2right)}^-2

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

Evaluate

$$-\frac{529}{36}\approx -14.694444444$$

Solution Steps

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

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

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{57}{4}.

$$-\frac{57}{4}-\left(\frac{3}{2}\right)^{-2}$$

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

$$-\frac{57}{4}-\frac{4}{9}$$

Subtract \frac{4}{9} from -\frac{57}{4} to get -\frac{529}{36}.

$$-\frac{529}{36}$$

Factor

$$-\frac{529}{36} = -14\frac{25}{36} = -14.694444444444445$$