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

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

Evaluate

$$\frac{19}{8}=2.375$$

Solution Steps

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

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

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

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

Calculate -3 to the power of -3 and get -\frac{1}{27}.

$$\frac{9}{4}-\frac{27}{8}\left(-\frac{1}{27}\right)$$

Multiply -\frac{27}{8} and -\frac{1}{27} to get \frac{1}{8}.

$$\frac{9}{4}+\frac{1}{8}$$

Add \frac{9}{4} and \frac{1}{8} to get \frac{19}{8}.

$$\frac{19}{8}$$

Factor

$$\frac{19}{2 ^ {3}} = 2\frac{3}{8} = 2.375$$