Solve (2/3)^2*(-3/2)^3*(-2/3)^6

$$( \frac { 2 } { 3 } ) ^ { 2 } \cdot ( - \frac { 3 } { 2 } ) ^ { 3 } \cdot ( - \frac { 2 } { 3 } ) ^ { 6 }$$

Evaluate

$$-\frac{32}{243}\approx -0.131687243$$

Solution Steps

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

$$\frac{4}{9}\left(-\frac{3}{2}\right)^{3}\left(-\frac{2}{3}\right)^{6}$$

Calculate -\frac{3}{2} to the power of 3 and get -\frac{27}{8}.

$$\frac{4}{9}\left(-\frac{27}{8}\right)\left(-\frac{2}{3}\right)^{6}$$

Multiply \frac{4}{9} times -\frac{27}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\left(-27\right)}{9\times 8}\left(-\frac{2}{3}\right)^{6}$$

Do the multiplications in the fraction \frac{4\left(-27\right)}{9\times 8}.

$$\frac{-108}{72}\left(-\frac{2}{3}\right)^{6}$$

Reduce the fraction \frac{-108}{72} to lowest terms by extracting and canceling out 36.

$$-\frac{3}{2}\left(-\frac{2}{3}\right)^{6}$$

Calculate -\frac{2}{3} to the power of 6 and get \frac{64}{729}.

$$-\frac{3}{2}\times \frac{64}{729}$$

Multiply -\frac{3}{2} times \frac{64}{729} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-3\times 64}{2\times 729}$$

Do the multiplications in the fraction \frac{-3\times 64}{2\times 729}.

$$\frac{-192}{1458}$$

Reduce the fraction \frac{-192}{1458} to lowest terms by extracting and canceling out 6.

$$-\frac{32}{243}$$

Factor

$$-\frac{32}{243} = -0.13168724279835392$$