Resolver =[(3/4)^-1-(3/2)^2]^-2

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

Avaliar

$$\frac{144}{121}\approx 1,190082645$$

Passos Para a Resolução

Calcule \frac{3}{4} elevado a -1 e obtenha \frac{4}{3}.

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

Calcule \frac{3}{2} elevado a 2 e obtenha \frac{9}{4}.

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

Subtraia \frac{9}{4} de \frac{4}{3} para obter -\frac{11}{12}.

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

Calcule -\frac{11}{12} elevado a -2 e obtenha \frac{144}{121}.

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

Fatorizar

$$\frac{2 ^ {4} \cdot 3 ^ {2}}{11 ^ {2}} = 1\frac{23}{121} = 1,1900826446280992$$