Solve -9/2[5/2:(-5/9)]^-2=

$$- \frac { 9 } { 2 } [ \frac { 5 } { 2 } : ( - \frac { 5 } { 9 } ) ] ^ { - 2 } =$$

Evaluate

$$-\frac{2}{9}\approx -0.222222222$$

Solution Steps

Divide \frac{5}{2} by -\frac{5}{9} by multiplying \frac{5}{2} by the reciprocal of -\frac{5}{9}.

$$-\frac{9}{2}\times \left(\frac{5}{2}\left(-\frac{9}{5}\right)\right)^{-2}$$

Multiply \frac{5}{2} and -\frac{9}{5} to get -\frac{9}{2}.

$$-\frac{9}{2}\left(-\frac{9}{2}\right)^{-2}$$

Calculate -\frac{9}{2} to the power of -2 and get \frac{4}{81}.

$$-\frac{9}{2}\times \frac{4}{81}$$

Multiply -\frac{9}{2} and \frac{4}{81} to get -\frac{2}{9}.

$$-\frac{2}{9}$$

Factor

$$-\frac{2}{9} = -0.2222222222222222$$