Solve {left(61/2right)}^3-21^2/4-1

$${ \left(6 \frac{ 1 }{ 2 } \right) }^{ 3 } -2 \frac{ { 1 }^{ 2 } }{ 4 } -1$$

Evaluate

$$\frac{2185}{8}=273.125$$

Solution Steps

Multiply 6 and 2 to get 12.

$$\left(\frac{12+1}{2}\right)^{3}-2\times \frac{1^{2}}{4}-1$$

Add 12 and 1 to get 13.

$$\left(\frac{13}{2}\right)^{3}-2\times \frac{1^{2}}{4}-1$$

Calculate \frac{13}{2} to the power of 3 and get \frac{2197}{8}.

$$\frac{2197}{8}-2\times \frac{1^{2}}{4}-1$$

Calculate 1 to the power of 2 and get 1.

$$\frac{2197}{8}-2\times \frac{1}{4}-1$$

Multiply 2 and \frac{1}{4} to get \frac{1}{2}.

$$\frac{2197}{8}-\frac{1}{2}-1$$

Subtract \frac{1}{2} from \frac{2197}{8} to get \frac{2193}{8}.

$$\frac{2193}{8}-1$$

Subtract 1 from \frac{2193}{8} to get \frac{2185}{8}.

$$\frac{2185}{8}$$

Factor

$$\frac{5 \cdot 19 \cdot 23}{2 ^ {3}} = 273\frac{1}{8} = 273.125$$