Solve (-3/2)^-1*(2/3)^2/(frac{2{3})^-1div(3/2)}

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

Evaluate

$$-\frac{8}{27}\approx -0.296296296$$

Solution Steps

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

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

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

$$\frac{-\frac{2}{3}\times \frac{4}{9}}{\frac{\left(\frac{2}{3}\right)^{-1}}{\frac{3}{2}}}$$

Multiply -\frac{2}{3} and \frac{4}{9} to get -\frac{8}{27}.

$$\frac{-\frac{8}{27}}{\frac{\left(\frac{2}{3}\right)^{-1}}{\frac{3}{2}}}$$

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

$$\frac{-\frac{8}{27}}{\frac{\frac{3}{2}}{\frac{3}{2}}}$$

Divide \frac{3}{2} by \frac{3}{2} to get 1.

$$\frac{-\frac{8}{27}}{1}$$

Anything divided by one gives itself.

$$-\frac{8}{27}$$

Factor

$$-\frac{8}{27} = -0.2962962962962963$$