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

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

Evaluate

$$-\frac{8}{81}\approx -0.098765432$$

Solution Steps

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

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

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

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

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

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

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

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

Add \frac{3}{2} and \frac{3}{2} to get 3.

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

Express \frac{-\frac{8}{27}}{3} as a single fraction.

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

Multiply 27 and 3 to get 81.

$$\frac{-8}{81}$$

Fraction \frac{-8}{81} can be rewritten as -\frac{8}{81} by extracting the negative sign.

$$-\frac{8}{81}$$

Factor

$$-\frac{8}{81} = -0.09876543209876543$$