Solve (-8/27)^-2-(-3/2)^-3

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

Evaluate

$$\frac{20195}{1728}\approx 11.686921296$$

Solution Steps

Calculate -\frac{8}{27} to the power of -2 and get \frac{729}{64}.

$$\frac{729}{64}-\left(\frac{-3}{2}\right)^{-3}$$

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

$$\frac{729}{64}-\left(-\frac{3}{2}\right)^{-3}$$

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

$$\frac{729}{64}-\left(-\frac{8}{27}\right)$$

The opposite of -\frac{8}{27} is \frac{8}{27}.

$$\frac{729}{64}+\frac{8}{27}$$

Add \frac{729}{64} and \frac{8}{27} to get \frac{20195}{1728}.

$$\frac{20195}{1728}$$

Factor

$$\frac{5 \cdot 7 \cdot 577}{2 ^ {6} \cdot 3 ^ {3}} = 11\frac{1187}{1728} = 11.686921296296296$$