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

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

Evaluate

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

Solution Steps

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

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

Subtract 2 from 5 to get 3.

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

Calculate 3 to the power of 3 and get 27.

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

Add \frac{27}{8} and 27 to get \frac{243}{8}.

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

Calculate \frac{9}{2} to the power of 2 and get \frac{81}{4}.

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

Add \frac{243}{8} and \frac{81}{4} to get \frac{405}{8}.

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

Subtract 1 from \frac{5}{2} to get \frac{3}{2}.

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

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

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

Subtract \frac{9}{4} from \frac{405}{8} to get \frac{387}{8}.

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

Factor

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