Solve [(3/4)^-1-(3/2)^2]^-2

$$[ ( \frac { 3 } { 4 } ) ^ { - 1 } - ( \frac { 3 } { 2 } ) ^ { 2 } ] ^ { - 2 }$$

Evaluate

$$\frac{144}{121}\approx 1.190082645$$

Solution Steps

Calculate \frac{3}{4} to the power of -1 and get \frac{4}{3}.

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

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

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

Subtract \frac{9}{4} from \frac{4}{3} to get -\frac{11}{12}.

$$\left(-\frac{11}{12}\right)^{-2}$$

Calculate -\frac{11}{12} to the power of -2 and get \frac{144}{121}.

$$\frac{144}{121}$$

Factor

$$\frac{2 ^ {4} \cdot 3 ^ {2}}{11 ^ {2}} = 1\frac{23}{121} = 1.1900826446280992$$