Resolver (3:2)^3+(5-2)^3+(9:2)^2-(5/2-1)^2=

$$( 3 : 2 ) ^ { 3 } + ( 5 - 2 ) ^ { 3 } + ( 9 : 2 ) ^ { 2 } - ( \frac { 5 } { 2 } - 1 ) ^ { 2 } =$$

Calcular

$$\frac{387}{8}=48.375$$

Pasos da solución

Calcula \frac{3}{2} á potencia de 3 e obtén \frac{27}{8}.

$$\frac{27}{8}+\left(5-2\right)^{3}+\left(\frac{9}{2}\right)^{2}-\left(\frac{5}{2}-1\right)^{2}$$

Resta 2 de 5 para obter 3.

$$\frac{27}{8}+3^{3}+\left(\frac{9}{2}\right)^{2}-\left(\frac{5}{2}-1\right)^{2}$$

Calcula 3 á potencia de 3 e obtén 27.

$$\frac{27}{8}+27+\left(\frac{9}{2}\right)^{2}-\left(\frac{5}{2}-1\right)^{2}$$

Suma \frac{27}{8} e 27 para obter \frac{243}{8}.

$$\frac{243}{8}+\left(\frac{9}{2}\right)^{2}-\left(\frac{5}{2}-1\right)^{2}$$

Calcula \frac{9}{2} á potencia de 2 e obtén \frac{81}{4}.

$$\frac{243}{8}+\frac{81}{4}-\left(\frac{5}{2}-1\right)^{2}$$

Suma \frac{243}{8} e \frac{81}{4} para obter \frac{405}{8}.

$$\frac{405}{8}-\left(\frac{5}{2}-1\right)^{2}$$

Resta 1 de \frac{5}{2} para obter \frac{3}{2}.

$$\frac{405}{8}-\left(\frac{3}{2}\right)^{2}$$

Calcula \frac{3}{2} á potencia de 2 e obtén \frac{9}{4}.

$$\frac{405}{8}-\frac{9}{4}$$

Resta \frac{9}{4} de \frac{405}{8} para obter \frac{387}{8}.

$$\frac{387}{8}$$

Factorizar

$$\frac{3 ^ {2} \cdot 43}{2 ^ {3}} = 48\frac{3}{8} = 48.375$$