Solve [(-2/3)^-1*(+3/2)^2(-2/3)^-3]:(-2/3)^-3

$$[ ( - \frac { 2 } { 3 } ) ^ { - 1 } \cdot ( + \frac { 3 } { 2 } ) ^ { 2 } ( - \frac { 2 } { 3 } ) ^ { - 3 } ] : ( - \frac { 2 } { 3 } ) ^ { - 3 }$$

Evaluate

$$-\frac{27}{8}=-3.375$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -1 and -3 to get -4.

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

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

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

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

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

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

$$\frac{\frac{9}{4}}{-\frac{2}{3}}$$

Divide \frac{9}{4} by -\frac{2}{3} by multiplying \frac{9}{4} by the reciprocal of -\frac{2}{3}.

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

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

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

Factor

$$-\frac{27}{8} = -3\frac{3}{8} = -3.375$$